# MGMT 300 Roosevelt University Production Problem Linear Programming Model Operations Management Worksheet

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#### Case: Production Problem, using Linear Programming Model:

The manager at ABC Company wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit. Production requirements for the products are shown in the following table:

Products: | |||

Requirements/Units: | A | B | C |

Material 1 (pounds) | 2 | 1 | 6 |

Material 2 (pounds) | 3 | 5 | 0 |

Labor (hours) | 3.2 | 1.5 | 2 |

Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product A sells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Available resources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.

The manager must satisfy certain output requirements: The output of product A should not be more than one-third of the total number of units produced; the ratio of units of product A to units of product B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem and then use solver to solve it, and answer the following questions:

- Are any constraints binding? If so, which one(s)?
- If the price of product C were changed to $75 a unit, what would the values of the decision variables be? The objective function? Explain.
- If the price on product A were changed to $85 a unit, what would the values of the decision variables be? The objective function? Explain.
- If 15 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain.
- If price per unit on each product increased by $5, would the optimal values of the decision variables change? Explain. What would the optimal value of the objective function be?

Submit your Excel worksheet along with your answers to these questions (in text boxes). Make sure to include your name in cell A1 and include your name in the file name.

(Answers are online can you complete and make the spread sheet)

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