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Mat540 quiz 3

Question # 00006836
Subject: Mathematics
Due on: 01/29/2014
Posted On: 01/18/2014 10:21 PM

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Quiz 3

Question 1




Surplus variables are only associated with minimization problems.

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Question 2




A feasible solution violates at least one of the constraints.

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Question 3




A linear programming model consists of only decision variables and constraints.

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Question 4




Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

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Question 5




If the objective function is parallel to a constraint, the constraint is infeasible.

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Question 6




A linear programming problem may have more than one set of solutions.

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Question 7




In minimization LP problems the feasible region is always below the resource constraints.

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Question 8




The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.This linear programming problem is a:

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Question 9




The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.The equation for constraint DH is:

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Question 10




The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.Which of the following constraints has a surplus greater than 0?

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Question 11




Which of the following statements is not true?

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Question 12




Decision variables

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Question 13




The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

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Question 14




The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function?

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Question 15




The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

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Question 16




Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?

Answer









Question 17




Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

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Question 18




A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation.

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Question 19




Solve the following graphicallyMax z = 3x1 +4x2s.t. x1 + 2x2 ? 16 2x1 + 3x2 ? 18 x1 ? 2 x2 ? 10 x1, x2 ? 0Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

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Question 20




Consider the following minimization problem: Min z = x1 + 2x2s.t. x1+ x2 ? 300 2x1 + x2 ? 400 2x1 + 5x2 ? 750 x1, x2 ? 0Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

Answer




Tags quiz mat540 answer question soft case solution regular production drink gallons minutes syrup diet shelf space optimal objective linear function storage programming requires following problem feet cubic limited profits medium

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Mat540 quiz 3

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Quiz_3_mat540.docx (67.38 KB)
Preview: Graphical xxxxxxxxx to xxxxxx programming problems xxxx an infinite xxxxxx of xxxxxxxx xxxxxxxxx function xxxxx Answer Correct xxxxxxx TrueQuestion 5 xx the xxxxxxxxx xxxxxxxx is xxxxxxxx to a xxxxxxxxxxx the constraint xx infeasible xxxxxx xxxxxxx Answer: xxxxxxxxxxxxx 6 A xxxxxx programming problem xxx have xxxx xxxx one xxx of solutions xxxxxx Correct Answer: xxxxxxxxxxxx 7 xx xxxxxxxxxxxx LP xxxxxxxx the feasible xxxxxx is always xxxxx the xxxxxxxx xxxxxxxxxxx Answer xxxxxxx Answer: FalseQuestion x The following xx a xxxxx xx a xxxxxx programming problem xxx feasible solution xxxxx is xxxxxxx xxx the xxxxxxx solution is xx the point xxxxxxx Z* xxxx xxxxxx programming xxxxxxx is a:Answer xxxxxxx Answer:minimization problemQuestion x The xxxxxxxxx xx a xxxxx of a xxxxxx programming problem xxx feasible xxxxxxxx xxxxx is xxxxxxx and the xxxxxxx solution is xx the xxxxx xxxxxxx Z* xxx equation for xxxxxxxxxx DH is:Answer xxxxxxx Answer:X x xx ? xxxxxxxxx 10 The xxxxxxxxx is a xxxxx of x xxxxxx programming xxxxxxx The feasible xxxxxxxx space is xxxxxxx and xxx xxxxxxx solution xx at the xxxxx labeled Z* xxxxx of xxx xxxxxxxxx constraints xxx a surplus xxxxxxx than 0?Answer xxxxxxx Answer:DHQuestion xx xxxxx of xxx following statements xx not true?Answer.....
Quiz_31.docx (25.99 KB)
Preview: case xxxxx 4 xxxxxxx and 3 xxxxxxx of syrup xxxxxxx for xxxxxxx xxxx drink xxx $3 00 xxx case and xxxxxxx for xxxx xxxx drink xxx $2 00 xxx case What xx the xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx Answer:MAX xxx + $2DQuestion xx The production xxxxxxx for xxx xxxxx soft xxxxx company is xxxxxxxxxxx the production xx 2 xxxxx xx soft xxxxxxx regular and xxxx Two of xxx limited xxxxxxxxx xxx production xxxx (8 hours x 480 minutes xxx day) xxx xxxxx (1 xx her ingredients) xxxxxxx to 675 xxxxxxx per xxx xx produce x regular case xxxxxxxx 2 minutes xxx 5 xxxxxxx xx syrup, xxxxx a diet xxxx needs 4 xxxxxxx and x xxxxxxx of xxxxx Profits for xxxxxxx soft drink xxx $3 xx xxx case xxx profits for xxxx soft drink xxx $2 xx xxx case xxx the production xxxxxxxxxxx of 135 xxxxx of xxxxxxx xxx 0 xxxxx of diet xxxx drink, which xxxxxxxxx will xxx xx completely xxxxxxxxxxx Correct Answer:only xxxxxxxxxxxx 16 Cully xxxxxxxxx buys x xxxxxxxx for xxxxxxx big shelves xxx and medium xxxxxxx (M) xxxx xxx shelf xxxxx $500 and xxxxxxxx 100 cubic xxxx of xxxxxxx xxxxxx and xxxx medium shelf xxxxx $300 and xxxxxxxx 90 xxxxx xxxx.....
Week_3_-_Quiz_2_Retake.docx (136.68 KB)
Preview: an xxxxxxxx in xxx price of xxxxx that was xxx result xx xxxxxxxxx demand xxx refrigerators 2 xxxxxx Question 8 x perfectly xxxxxxx xxxxxx curve xxxxxxxxxxx be a xxxxxxxx straight line xx a xxxxxxxx xxxxxxx straight xxxx be a xxxxxxxxxx straight line xx an xxxxxx xxxxxxx straight xxxx 2 points xxxxxxxx 9 Which xx the xxxxxxxxx xxxxxxxxxxx can xx considered as xx inferior good?Answer xxxxxxxx in x xxxxx apartment xxxxxxx in a xxxxxxxxxxxxx clothes in x washer xx xxxxxxxxxx out xx an upscale xxxxxxxxxxxxxxxxxx vacations at xxxxxx locations2 xxxxxx xxxxxxxx 10 xxx market-clearing price xxxxxxxxx the price xx which xxx xxxxxx is xx equilibrium the xxxxx at which xxxxxxxx beneficial xxxxx xxxx place xxx price at xxxxx sellers earn xxx maximum xxxxxx xxx price xx which consumer xxxxxxx is zero x points xxxxxxxx xx A xxxxxxx can exist xx the market xxxx if xxxxx xxxxxxxxx a xxx binding price xxxxx a binding xxxxx floor x xxxxxxx price xxxxxxx a non xxxxxxx price ceiling x points xxxxxxxx xx Suppose xxx adoption of x new software xxxxxxx the xxxxxxxx xxxx of xxxxxxxxxx books For x given demand xxxxx for xxxxxx xxxx will xx represented by:Answer xx upward movement xxxxx the xxxxxx xxxxx of xxxxx a downward xxxxxxxx along the xxxxxx curve xx xxxxx an xxxxxx shift in xxx supply curve xx books x xxxxxxxx shift xx the supply xxxxx of books x points xxxxxxxx xx The xxxx above the xxxxxx curve and xxxxx the xxxxxx xxxxx represents:Answer xxx consumer surplusthe xxxxxxxx surplus the xxxxxxxxxx loss xx xxx producer xxx deadweight loss xx the consumer x points xxxxxxxx xx Starting xxxx a pure xxxxxxxx equilibrium, an xxxxxxxx in xxx xxxxxx for x commodity will xxxxxx in:Answer a xxxx in xxx xxxxxx price x rise in xxx market price x rise xx xxx equilibrium xxxxxx a fall xx the equilibrium xxxxxx 2 xxxxxx xxxxxxxx 15 xxx contact points xxxxx the terms xx forward xxxxxxxxx xxx set xxx known as:Answer xxx underlying markets xxx derivative.....
ch02_(1).doc (305 KB)
Preview: product x is xxxxxxxxxxx and on xxxxxxx 2 is xxxxxxxxxxx The xxxxxxxxxxx xx these xxxxxxxx depends largely xx the availability xx certain xxxxxxxxxxxxx xxx plant xxxxxxxx daily from x local distributor xx takes xxxxx xx these xxxxxxxxxxxxx for each xxxx of product x and xxx xxx each xxxx of product x Twelve such xxxxxxxxxxxxx are xxxxxxxxx xxxxx Further, xx takes two xxxxx to make x unit xx xxxxxxx 1 xxx six hours xx make a xxxx of xxxxxxx x The xxxxx has assigned xxxx three workers xxxxxxx 8-hour xxxxxx xxx these xxx products Due xx limited demand, xxx manager xxxx xxx want xxxx than seven xxxxx of product x produced xxxxx xx Formulate xxxx problem as x linear program xx Solve xxxxxxxxxxx xxx the xxxxxxx solution Describe xxx set of xxx optimal xxxxxxxxx xxxxxxxx any xxxxxxxxx constraints c) xxxx an optimal xxxxx production xxxxxxxx xxxx manufactures xxxxxxx one unit xx product 1 xx Discuss xxx xxxxxxxxxxxxx of xxxxxx programming for xxxx problem SOLUTION x a) xxx xxxxxx variables xx and x2 xxx amount of xxxxxxx 1 xxx x produced xxxxx (2) Define xxxxxxxxx Maximize total xxxxx profits xxx xxx 3x2 xxx thousands of xxxxxxxx (3) Define xxxxxxxxxxx Subassemblies xxxxxx xxxx daily xxxxxx available 3x1 xxx 12 Labor xxxxxx of xxxxx xxxx daily xx men)x(8 hrs xxxxx 2x1 6x2 xx Product x xxxxxxxx produced xxxxx specified limit xx 7 Non-negativity xx variables xxx xx 0 xxxxxxxxxxxx MAX z xxx 3x2 s x 3x1 xxx xx 2x1 xxx 24 x2 x x1, x2 x b) xxxxxxxxxxxx xxxxx Word xxxxxxx 8 The xxxxxxx solution occurs xx x1 xx xx 4 xxx at x1 xxxxx x2 24/7, xxx at xxx xxxxxx in xxxxxxx on the xxxx 2x1 6x2 xx At xxx xxxxx on xxxx line, z xx The x2 x constraint xxxx xxx help xxxxx the feasible xxxxxx and thus xx redundant xx xx the xxxxxxx solution line, xxx 6x2 24, xxxx x1 xx xxxx x2 xxxx Still, z xxxx 3(11/3) 12 xxxxxxxxxx d) xxx xxxx consider xxxxxxx these variables xxx be allowed xx assume xxxxxx xxxxx are xxx integers For xxxxxxxxxx production, frequently x fractional xxxxx xxx be xxxxxxxxxx as work xx progress products xxx finished xx xxx day xxx simply completed xxx next day xxxxx LP xxxxxxx xx be xxxxxxxxxxx for this xxxxxxx PROBLEM 8 x small xxxxxxx xxxx be xxxxxxxxxxx a new xxxx of lightweight xxxxxxx frames xx xx made xxxx special aluminum xxx steel alloys xxx frames xxxx xx produced xx two models, xxxxxx and professional, xxxx anticipated xxxx xxxxxxx of xx and 15, xxxxxxxxxxxx The number xx pounds xx xxxxxxxx alloy xxx steel alloy xxxxxx per deluxe xxxxx is x xxx 3, xxxxxxxxxxxx The number xx pounds of xxxxxxxx alloy xxx xxxxx alloy xxxxxx per professional xxxxx is 4 xxx 2, xxxxxxxxxxxx x supplier xxxxxxxx 100 pounds xx the aluminum xxxxx and xx xxxxxx of xxx steel alloy xxxxxx What is xxx optimal xxxxxx xxxxxxxxxx schedule xxxxxxxx 8 Let xx and x2 xxxxx the xxxxxx xx deluxe xxx professional frames xxxxxxxx weekly MAX x 10x1 xxxx x t xxx 4x2 100 xxx 2x2 80 xxx x2 x xxxxxxx graphically, xxx optimal production xxxxxxxx is to xxxxxxx x1 xx .....
Multi2.doc (283 KB)
Preview: of xxxxxx programming xxxxxx FALSE Diff x Page Ref xx Main xxxxxxx xxxxxxxxxx of xxxxxx Programming Models xxx words graphical xxxxxxxxx proportionality xxx xxxxxxxxx functions xx linear programs xxxxxx minimize costs xxxxxx FALSE xxxx x Page xxx 30 Main xxxxxxx Properties of xxxxxx Programming xxxxxx xxx words xxxxxxxxxx of linear xxxxxxxxxxx models, objective xxxxxxxx 16) xxx xxxxxxxx solution xxxx contains infinite xxxxxxxxx to the xxxxxx program xxxxxx xxxx Diff x Page Ref xx Main Heading xxxxxxxxxx of xxxxxx xxxxxxxxxxx Models xxx words properties xx linear programming xxxxxxx feasible xxxxxxxx xxxx 17) xxxxx is exactly xxx optimal solution xxxxx to x xxxxxx program xxxxxx FALSE Diff x Page Ref xx Main xxxxxxx xxxxxxxxxx of xxxxxx Programming Models xxx words properties xx linear xxxxxxxxxxx xxxxxxx optimal xxxxxxxx pt Diff x Page Ref xxxxx Main xxxxxxx xxxxxxxxxx of xxxxxx Programming Models xxx words properties xx linear xxxxxxxxxxx xxxxxxx surplus xxxxxxxxx 20) In xxx graphical approach, xxxxxxxxxxxx equations xxx xx used xx solve for xxx optimal solution xxxxx Answer xxxx xxxx 2 xxxx Ref 34 xxxx Heading Graphical xxxxxxxxx of xxxxxx xxxxxxxxxxx Models xxx words graphical xxxxxxxx 21) Slack xxxxxxxxx are xxxx xxxxxxxxxx with xxxxxxxxxxxx problems Answer xxxxx Diff 2 xxxx Ref xx xxxx Heading xxxxxxxxx Solutions of xxxxxx Programming Models xxx words xxxxxxxxx xxxxxxxxx slack xxxxxxxxx 22) Surplus xxxxxxxxx are only xxxxxxxxxx with xxxxxxxxxxxx xxxxxxxx Answer xxxxx Diff 2 xxxx Ref 52 xxxx Heading xxxxxxxxx xxxxxxxxx of xxxxxx Programming Models xxx words graphical xxxxxxxxx surplus xxxxxxxx xxx If xxx objective function xx parallel to x constraint, xxx xxxxxxxxxx is xxxxxxxxxx Answer FALSE xxxx 2 Page xxx 53 xxxx xxxxxxx Graphical xxxxxxxxx of Linear xxxxxxxxxxx Models Key xxxxx graphical xxxxxxxx xxx Multiple xxxxxxx solutions occur xxxx constraints are xxxxxxxx to xxxx xxxxx Answer xxxxx Diff 2 xxxx Ref 53 xxxx Heading xxxxxxxxx xxxxxxxxx of xxxxxx Programming Models xxx words graphical xxxxxxxx 25) xxxxxxxxx xxxxxxxxx to xxxxxx programming problems xxxx an infinite xxxxxx of xxxxxxxx xxxxxxxxx function xxxxx Answer TRUE xxxx 2 Page xxx 34 xxxx xxxxxxx Graphical xxxxxxxxx of Linear xxxxxxxxxxx Models Key xxxxx graphical xxxxxxxxx xxxxxxxxx function xxxx 26) The xxxxx step in xxxxxxxxxxx a xxxxxx xxxxxxxxxxx model xx to define xxx objective function xxxxxx FALSE xxxx x Page xxx 32 Main xxxxxxx Management Science xxxxxxxx Techniques xxx xxxxx linear xxxxxxxxxxx problems, formulation xxx __________ are xxxxxxxxxxxx symbols xxxxxxxxxxxx xxxxxx of xxxxxxxx Answer Decision xxxxxxxxx Diff 1 xxxx Ref xx xxxx Heading xxxxx Formulation Key xxxxx decision variables, xxxxx formulation xxx xxx __________ xx a linear xxxxxxxxxxxx reflecting the xxxxxxxxx of xx xxxxxxxxx Answer xxxxxxxxx function Diff x Page Ref xx Main xxxxxxx xxxxx Formulation xxx words objective xxxxxxxxx model formulation xxx A xxxxxxxxxx xx a xxxxxx relationship repre.....
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