National University MNS407 Midterm Exam
MNS 407 Midterm Exam Last Name: _________________First Name:______ Class#:___
Part I: Multiple Choices: M/C; Each 4 points Total Points= 20
_____ 1.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.
If this is a minimization, which extreme point is the optimal solution?
a) Point D b) Point C c) Point B d) Point A e)) None of the Above
_____ 2.A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 lbs. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is: | ||||||||||
a) x1 ? 8, x2 ? 8, x3 ? 8 | ||||||||||
b) 4x1+ 3x2 + 2x3 ? 24 | ||||||||||
c) x1 ? 6, x2 ? 8, x3 ? 12 | ||||||||||
d) x1+ x2 + x3 ? 24 | ||||||||||
e) x1+ x2 + x3 ? 24 | ||||||||||
_____3. Larry’s Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is:
| ||||||||||
_____ 4.Decision variables:
a) Measure the objective function |
b) Measure the values of each constraint |
c) Always exist for each constraint |
d) Measure how much or how many items to produce, purchase, hire, etc |
e) None of the Above
_____ 5.Given the following linear programming model, identify the optimal solution.
Maximize Z = $18x1 + $14x2
Subject to: 1) 4x1 + 2x2 < or = 80
2) 2x1 + 6x2 < or = 60
a) No Solution
b) x1 = 5, x2 = 6, Z = 174
c) x1 = 30, x2 = 1, Z = 554
d) x1 = 15, x2 = 5, Z = 340
e) x1 = 18, x2 = 4, Z =380
Part II. Solve the Problems; Total points = 80
1. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two
resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per
week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12
oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat.
Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. If the
production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer,
it will result in slack of
A) malt only
B) wheat only
C) both malt and wheat
D) neither malt nor wheat
Write the formulation for this linear program And Explain
2.Consider the following linear programming problem:
Max Z = $30x + $40y
Subject to: 16x + 10y ? 80
0.8x + 2y ? 8
x, y ? 0
Determine the values for x and y that will maximize revenue. Show by Graph.
3.What combination of x and y will provide a feasible solution and a minimum objective
function value for the following problem?
Min Z = 3x + 15y
(1) 2x + 4y ? 12
(2) 5x + 2y ?10
Show by Graph the optimal solution,. Explain in detail of your work
4.Max Z = 5x1 + 3x2
Subject to: 6x1 + 2x2 ? 18
Find the optimal profit and the values of x1 and x2 at the optimal solution .Use Graph to estimate the Profit;
Explain in detail of your work
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Solution: National University MNS407 Midterm Exam