Solved by verified expert:1. Please DO NOT USE EXCEL OR ANY COMPUTER SOFTWARE OR WEBSITE to solve the problems or to draw graphs. 2. Show all work. 3.Make sure you have answered all six questions. 4. Please submit the exam in Microsoft Word. Scans or photos of theanswers are acceptable but they must be clear and legible. Other formats are not acceptable.

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1. Please DO NOT USE EXCEL OR ANY COMPUTER SOFTWARE OR WEBSITE to solve the

problems or to draw graphs.

2. Show all work.

3. Make sure you have answered all six questions.

4. Please submit the exam in Microsoft Word. Scans or photos of theanswers are acceptable but they

must be clear and legible. Other formats are not acceptable.

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

steps needed in each method.

(b) What are the different types of special situations that may occur while solving a linear programming

problem? Briefly describe each of these special situations and give one example for each special situation.

(c) What are the important properties of a straight line? Briefly describe each property. What are the different

types of slopes possible for a straight line? Briefly describe each type of slope and give one example for each

type.

(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 25x + 20y

Subject to

x + y < 50
2x + 3y < 120
x, y > 0

(a) Graph the constraints and find the feasible region.

(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 = 10 and y = 10, state the

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

Maximize 5x + 4y

Subject to

4x + 2y ≤ 80

3x + 5y ≥ 60

x ≤ 10

y ≤ 10

x, y > 0

1

4. A company manufactures two kinds of pinball machines, each requiring a different manufacturing

technique. Each Super Ball machine requires 25 hours of labor, 6 hours of testing, and yields a profit of $400.

Each Silver Ball machine requires 15 hours of labor, 8 hours of testing, and yields a profit of $250. There are

2250 hours of labor and 1200 hours of testing available.

The company has made contracts with the retailers to provide at least 50 Super Ball machines and at least 46

Silver Ball machines. The company does not want to make more than a total of 120 of the two machines

combined.

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

to maximize the total profit.

Formulate a linear programming model for the above situation by determining

(a) 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.

5. Charming City Foods manufactures a snack bar by blending two ingredients: a nut mix and a granola mix.

Information about the two ingredients (per ounce) is shown below.

Ingredient

Nut Mix

Granola Mix

Cost In Dollars

0.90

0.50

Fat Grams

24

4

Protein Grams

8

3

Calories

650

60

The company needs to develop a linear programming model whose solution would tell them how many

ounces of each mix to put into the snack bar. The blend should contain no more than 1100 calories, at least 12

grams of protein, and no more than 32 grams of fat. In addition, at least one ounce of nut mix must be

included in the blend. The objective is to minimize the total cost of a snack bar.

Formulate a linear programming model for the above situation by determining

(a) 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.

Minimize 15x + 20y

Subject to:

2x + y < 15
x + 2y > 20

y<5
x, y > 0

2

…

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