# Determine the production quantities through linear programming

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Indicate whether the sentence or statement is true or false.

_____ 1. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.

_____ 2. When using linear programming model to solve the "diet" problem, the objective is generally to maximize profit.

_____ 3. The standard form for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

_____ 4. 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.

_____ 5. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

Identify the letter of the choice that best completes the statement or answers the question.

_____ 6. Which solutions are ones that satisfy all the constraints simultaneously?

a. alternate

b. feasible

c. infeasible

d. optimal

_____ 7. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 200 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of salt. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50. What is the objective function?

a. Z = $0.50L + $0.40V

b. Z = $0.40L + $0.50V

c. Z = $0.20L + $0.30V

d. Z = $0.30L + $0.20V

_____ 8. Profit is maximized in the objective function by

a. subtracting cost from revenue

b. subtracting revenue from cost

c. adding revenue to cost

d. multiplying revenue by cost

_____ 9. 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.

a. x21 + x22 <= 8000

b. x12 + x22 >= 8000

c. X11 + x12 <= 8000

d. X12 + x22 <= 8000

_____ 10. A systematic approach to model formulation is to first

a. construct the objective function

b. develop each constraint separately

c. define decision variables

d. determine the right hand side of each constraint

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(See attached file for full problem description)

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#### Solution Summary

This helps to determine the truth of several statements regarding linear programming and also briefly shows how to set up linear programming problems.

Operations research and Linear programming

I need help finding the constraints for this problem as well as solutions to part d and c.

(See attached file for full problem description)

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Benson Electronics manufactures a number of components and products for a variety of commercial applications. Each product places different demands on the various departments within the company. In one instance, Benson manufactures three components used to produce cellular telephones and other communication devices. In a given production period, demand for the three components may exceed Benson's overall manufacturing capacity. In this case, the company meets demand by purchasing the components from another manufacturer at an increased cost per unit. Benson's manufacturing cost per unit and purchasing cost per unit for the three components are as follows:

Source Component 1 Component 2 Component 3

Manufacture $3.50 $6.00 $3.75

Purchase $5.50 $9.80 $7.00

Manufacturing times in minutes per unit for Benson's three departments are as follows:

Department Component 1 Component 2 Component 3

Production 2 3 4

Assembly 1 1.5 3

Testing and Packaging 1.5 2 5

For example, each unit of component 1 that Benson manufactures requires 2 minutes of production time, 1 minute of assembly time, and 1.5 minutes of testing and packaging time. For the next production period, Benson has capacities of 360 hours in the production department, 250 hours in the assembly department, and 300 hours in the testing and packaging department. Component demands that must be satisfied are 6000 units for component 1, 4000 units for component 2, and 3500 units for component 3.

a. Formulate a linear programming model that can be used to determine how many units of each component to manufacture and how many units of each component to purchase.

b. Determine the optimal plan that minimizes the total manufacturing and purchasing costs, including the number units of each component to be manufactured and the number units of each component to be purchased.

c. Determine which departments, if any, are limiting Benson's manufacturing quantities. Use the dual prices to determine the value of an extra hour in each of these departments. Determine the level of unused capacity, if any, resulting from the optimal schedule for each of the associated departments.

d. Suppose that Benson needs to obtain one additional unit of component 1. Interpret what the dual price for the component 2 constraint illustrates with respect to the cost to obtain the additional unit.

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