# Multiplant Operation Problem

1) Appalachia Beverage Company, Inc. is considering alternative proposals for expansion into the Midwest.

Alternative # 1: Construct a single plant in Indianapolis, Indiana, with a monthly production capacity of 300,000 cases, a monthly fixed cost of $262,500, and a variable cost of $3.25 per case.

Alternative # 2: Construct three plants, one each in Muncie, Indiana; Normal, Illinois; and Dayton, Ohio, with capacities of 120,000, 100,000, and 80,000, respectively, and monthly fixed costs of $120,000, $110,000, and $95,000 each. Variable costs would be only $3 per case because of lower distribution costs. To achieve these cost savings, sales from each smaller plant would be limited to demand within its home state. The total estimated monthly sales volume of 200,000 cases in these three Midwestern states is distributed as follows: 80,000 cases in Indiana, 70,000 cases in Illinois, and 50,000 cases in Ohio.

A. Assuming a wholesale price of $5 per case, calculate the breakeven output quantities for each alternative.

B. At a wholesale price of $5 per case in all states, and assuming sales at the projected levels, which alternative expansion scheme provides Appalachia with the highest profit per month?

C. If sales increase to production capacities, which alternative would prove to be more profitable?

2) Is the use of the least-cost input combinations a necessary condition for profit maximization? Is it a sufficient condition? Explain.

3) Explain why the MP/P relation is deficient as the sole mechanism for determining the optimal level of resource employment.

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#### Solution Preview

See attached Excel file for calculations.

1)

Alternative # 2

A. Assuming a wholesale price of $5 per case, calculate the breakeven output quantities for each alternative.

Single plant: 150,000. Indiana: 60,000 Illinois: 55,000 Ohio: 47500

(See excel for detail)

B. At a wholesale price of $5 per case in all states, and assuming ...

#### Solution Summary

This posting briefly explains why the MP/P relation is deficient as the sole mechanism for determining the optimal level of resource employment as well as other functions. 196 words.