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# Linear programming MCQs and problems

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1. Decision variables
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint.

2. Which of the following is a valid objective function for a linear programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3

3. Which of the following statements is NOT true?
a. A feasible solution satisfies all constraints.
b. An optimal solution satisfies all constraints.
c. An infeasible solution violates all constraints.
d. A feasible solution point does not have to lie on the boundary of the feasible region.

4. To find the optimal solution to a linear programming problem using the graphical method
a. find the feasible point that is the farthest away from the origin.
b. find the feasible point that is at the highest location.
c. find the feasible point that is closest to the origin.
d. None of the alternatives is correct.

5. The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. dual price.
c. constraint coefficient.
d. slack value.

6. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is
a. at least 1.
b. 0.
c. an infinite number.
d. at least 2.

7. A constraint that does not affect the feasible region is a
a. non-negativity constraint.
b. redundant constraint.
c. standard constraint.
d. slack constraint.

8. All linear programming problems have all of the following properties EXCEPT
a. a linear objective function that is to be maximized or minimized.
b. a set of linear constraints.
c. alternative optimal solutions.
d. variables that are all restricted to nonnegative values.

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1. (50 points)

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below.

Medium Cost Per Ad # Reached Exposure Quality
TV 500 10000 30
Newspaper 400 5000 25

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is \$10000, develop the model that will maximize the number reached and achieve an exposure quality of at least 1000. Find the optimal solution using Management Scientist or Excel Solver

2. (50 points)

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these trikes.

As indicated in the table below, the company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles, so it has arranged to purchase additional components, as necessary. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost. Find the optimal solution using Management Scientist or Excel Solver

Requirements
Component Plastic Time Space Cost to Manufacture Cost to Purchase
Front 3 10 2 8 12
Seat/Frame 4 6 2 6 9
Each rear wheel .5 2 .1 1 3
Available 50000 160000 30000

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