Quantitative Business Analysis

Case Study - Son, Ltd

Stevenson, W. (2021), Operations Management, 14th. Ed., McGraw-Hill, pp. 861

Son, Ltd., manufactures a variety of chemical products used by photoprocessors. Son was recently bought out by a conglomer-ate, 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 meth-ods whenever possible. The manager of one department has been given a weekly operating budget of $11,980 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 in the table.
The company has a contractual obligation for 85 units of prod¬uct R per week.
Material A costs S4 per pound, as does material B. Labor costs S8 an hour.
Product Q sells for S122 a unit, product R sells for S115 a unit, and product W sells for S76 a unit.
The manager is considering a number of different proposals regarding the quantity of each product to produce. 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:

Question 1. The optimal quantities of products and the necessary quanti¬ties of labor and materials.

Question 2. One proposal is to make equal amounts of the products. What amount of each will maximize contribution, and what quantities of labor and materials will be needed? How much less will total contribution be if this proposal is adopted?

Question 3. How would you formulate the constraint for material A if it was determined that there is a 5 percent waste factor for material A and equal quantities of each product are required?