Strayer MAT540 week 9 quiz 4

Question 1

1. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.
   

   Answer

   True

   False

2 points

Question 2

1. When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit.
   

   Answer

   True

   False

2 points

Question 3

1. In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.
   

   Answer

   True

   False

2 points

Question 4

1. Product mix problems cannot have "greater than or equal to" (?) constraints.
   

   Answer

   True

   False

2 points

Question 5

1. A constraint for a linear programming problem can never have a zero as its right-hand-side value.
   

   Answer

   True

   False

2 points

Question 6

1. In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.
   

   Answer

   True

   False

2 points

Question 7

1. When systematically formulating a linear program, the first step is

   Answer

   		Construct the objective function
   		Formulate the constraints
   		Identify the decision variables
   		Identify the parameter values

2 points

Question 8

1. The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.
   

   Ingredient	Percent per pound in Feed A	Percent per pound in Feed B	Minimum daily requirement (pounds)
   1	20	24	30
   2	30	10	50
   3	0	30	20
   4	24	15	60
   5	10	20	40

   
   
   The constraint for ingredient 3 is:

   Answer

   		.5A + .75B = 20
   		.3B = 20
   		.3 B? 20
   		.3B ? 20

2 points

Question 9

1. Balanced transportation problems have the following type of constraints:

   Answer

   		?
   		?
   		=
   		all the above

2 points

Question 10

1. The following types of constraints are ones that might be found in linear programming formulations:

   1.	?
   2.	=
   3.	>

   Answer

   		1 and 2
   		2 and 3
   		1 and 3
   		all of the above

2 points

Question 11

1. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

   Answer

   		x21 + x22 ? 8000
   		x12 + x22 ? 8000
   		x11 + x12 ? 8000
   		x21 + x22 ? 8000

2 points

Question 12

1. In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is

   Answer

   		MAX .06X1 +.08X2 +.11X3
   		MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3
   		MAX 15X1 + 47.25X2 +.110X3
   		MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3

2 points

Question 13

1. A systematic approach to model formulation is to first

   Answer

   		construct the objective function
   		develop each constraint separately
   		define decision variables
   		all of the above

2 points

Question 14

1. A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit?

   Answer

   		$380
   		$400
   		$420
   		$440

2 points

Question 15

1. In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint?

   Answer

   		X2 ? 10000 X2 + X3 ?350
   		10,000 X2 ? 350X2 + 350X3
   		47.25X2 ?10,000 X2 + X3 ? 350
   		47.25X2 ?10,000 47.25 X2 + 110X3 ? 350

2 points

Question 16

1. The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) 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 optimal daily profit?

   Answer

   		$220
   		$420
   		$320
   		$280

2 points

Question 17

1. Compared to blending and product mix problems, transportation problems are unique because

   Answer

   		They maximize profit.
   		The constraints are all equality constraints with no "?" or "?" constraints.
   		They contain fewer variables.
   		The solution values are always integers.

2 points

Question 18

1. Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as:

   Answer

   		.4x2 - .6x7 - .6x8 ? 0
   		x2 ? .60 (x2 + x7 + x8)
   		.4x2 - .6x7 - .6x8 ? 0
   		-.4x2 + .6x7 + .6x8 ? 0

2 points

Question 19

1. Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows:
   
   
   
   Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan?Express your answer with two places to the right of the decimal point.For instance, $9.32(nine dollars and thirty-two cents) would be written as 9.32
   

   Answer

2 points

Question 20

1. Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How many gallons of water based paint should the Quickbrush make?Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate.
   

   Answer