Answer & Explanation:1.

For full or partial credit, show all work. Just writing the final answer will

not get you full credit.

2.

Write your name on each and every page

of the exam.

3.

Make sure you have answered all six

questions.

exam1__6_.doc

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1. For full or partial credit, show all work. Just writing the final answer will not get you full credit.

2. Write your name on each and every page of the exam.

3. Make sure you have answered all six questions.

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OPRE 315: Midterm Exam 1

All six questions are required.

Question 1: 32 Points

Question 2: 20 Points

Questions 3, 4, 5, and 6: 12 Points each

1. (a) What are the different graphical methods to solve a linear programming problem? Briefly describe the

steps needed in each method.

(b) What is an infeasible linear programming problem? How do we find if a given linear programming

problem is infeasible? Give a real world example of an infeasible linear programming problem.

(c) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a

slack and a surplus variable?

(d) Briefly describe the important parts of each step needed to make a decision using decision sciences

models.

2. Given the following linear programming problem

Maximize 20x + 18y

Subject to

x + y < 50
2x + 3y < 120
x > 10

x, y > 0

(a) Graph the constraints.

(b) Find the coordinates of each corner point of the feasible region

(c) Determine the optimal solution.

3. Given that the optimal solution of the following linear programming problem is x = 15 and y = 0, State the

problem in standard form and do a constraint analysis for the optimal solution.

Maximize 5x + 3y

Subject to

4x + 6y ≤ 60

6x + 5y ≥ 60

y≤4

x, y > 0

4. The Charm City Silver Ball Company manufactures three kinds of pinball machines, each requiring a

different manufacturing technique. The Super Machine requires 22 hours of labor, 12 hours of testing, and

yields a profit of $300. The Silver Ball Special requires 11 hours of labor, 7 hours of testing, and yields a

profit of $220. The Bumper King requires 7 hours of labor, 4 hours of testing, and yields a profit of $120.

There are 1400 hours of labor and 660 hours of testing available.

The company has made contracts with the retailers to provide at least 22 Super Machines, at least 25 Silver

Ball Specials, and at least 30 Bumper Kings.

The manufacturer wants to determine how many of each kind of pinball machines to manufacture. The

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objective is to maximize the total profit.

Formulate a linear programming model for the above situation by determining

(a) The decision variables (Hint: There are three decision variables for this problem)

(b) The objective function. What does it represent?

(c) All the constraints. What does it represent?

Note: Do NOT solve the problem after formulating.

5. The Texas Oil Company produces premium gasoline. Its gasoline is produced by blending two petroleum

components. The premium gasoline must have a minimum octane rating of 120. The octane ratings, cost per

gallon, and the availability of the two blending ingredients are given in the following table.

Blending Ingredient Octane Rating

Cost/gallon Available gallons

_________________________________________________________________

Component 1

135

$1.80

120,000

Component 2

95

1.25

90,000

_________________________________________________________________

Formulate an LP to determine the gallons of each blending ingredient to be used to produce the premium

gasoline. The objective is to minimize total cost.

(a) Define the decision variables.

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.

6. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple

optimal solutions. Draw a graph to find the feasible region (if it exists) and explain your conclusion.

Maximize 60x + 80y

Subject to:

x + y > 15

x > 12

y < 10
x, y > 0

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