Son, Ltd. manufactures variety of chemical products used by photo-processors. A conglomerate recently bought out Son, and managers of the two organizations have been working together to improve the efficiency of Son's operations.
Managers have been asked to adhere to weekly operating budgets and to develop operating plans using quantitative methods whenever possible. The manager of one department has been given a weekly operating budget of USD11,980 for production of three chemical products, which for convenience shall be referred to as Q, R, and W. The budget is intended to pay for direct labor and materials. Processing requirements for the three products, on a per unit basis, are shown below:
Product Labor (hours) Material A (pounds) Material B (pounds)
Q 5 2 1
R 4 2 -
W 2 1/2 2
The company has a contractual obligation for 85 units of product R per week.
Material A costs USD4 per pound, as does material B. Labor costs USD8 an hour.
Product Q sells foe USD122 a unit, product R sells for USD115 a unit, and product W sells for USD76 a unit.
The manager is primarily interested in maximizing contribution. Moreover, the manager wants to know how much labor will be needed, as well as the amount of each material to purchase.
Questions:
Prepare a report that addresses the following issues:
1. The optimal quanities of products and the necessary quantities of labor and material.
2. One proposal is to make equal amounts of the products.What amoun of each will maximize contribution, and what uantities of labor and materials will be needed? How much less will total contribution be if this proposal is adopted?
3. How would you formulate the constraint for material A if it was determined that there is a 5% wast factor for material A and equal quatities of each product are required?