Question

One of the products of the G. A. Tanner Company is a special kind of toy that provides an estimated unit profit of $3. Because of a large demand for this toy, management would like to increase its production rate from the current level of 1,000 per day. However, a limited supply of two subassemblies (A and B) from vendors makes this difficult. Each toy requires two subassemblies of type A, but the vendor providing these subassemblies would only be able to increase its supply rate from the current 2,000 per day to a maximum of 3,000 per day. Each toy requires only one subassembly of type B, but the vendor providing these subassemblies would be unable to increase its supply rate above the current level of 1,000 per day. Because no other vendors currently are available to provide these subassemblies, management is considering initiating a new production process internally that would simultaneously produce an equal number of subassemblies of the two types to supplement the supply from the two vendors. It is estimated that the company’s cost for producing one subassembly of each type would be $2.50 more than the cost of purchasing these subassemblies from the two vendors. Click here for the Excel Data File Toys Subassemblies Unit Profit $3.00 $(2.50) Resource Usage Subassembly A 2 (1) Subassembly B 1 (1) Formulate and solve a spreadsheet model for this problem. Then use solver’s sensitivity report to find the allowable range for the unit profit of each activity. Determine both the production rate of the toy and the production rate of each pair of subassemblies (one A and one B). Note: If an allowable increase/decrease is 10,000 or larger, simply enter 10,000. Negative values should be indicated by a minus sign. Round "Objective Coefficient" and "Allowable Decrease" answers to 1 decimal place.

Answer 1

The G. A. Tanner Company must optimize toy production and possibly produce subassemblies internally, despite higher costs, to meet demand. A Solver sensitivity report will yield the allowable unit profit range, and economies of scale may influence cost as production increases.

Step-by-step explanation:

The scenario provided involves the G. A. Tanner Company considering an increase in production of a profitable toy while facing limited supplies of necessary subassemblies from vendors. Each toy needs two type A and one type B subassemblies, but the supply of these components is constrained at 3,000 per day for subassembly A and at 1,000 per day for subassembly B, from external vendors. Due to these constraints, the company is contemplating manufacturing the subassemblies internally at an extra cost. Management is tasked with finding an optimal production rate for toys and supplemental in-house production of subassemblies to maximize profits while adhering to supply limitations.

A sensitivity report from Solver, an Excel tool, would help in determining the allowable range for unit profits considering changes in production costs. The optimization model will estimate the production and financial implications. Economies of scale are relevant to this scenario as increasing production internally may also lead to reduced average costs in comparison to smaller amounts, as illustrated in various examples provided regarding the production cost differences at different factory outputs.