Constrained Optimization Analysis: Product-Mix Decision Sandalwood Company produces variou...

Constrained Optimization Analysis: Product-Mix Decision Sandalwood Company produces various lines of high-end carpeting in its Asheville, North Carolina, plant. This question pertains to two different grades of carpet in its Symphony line: commercial and residential. The former sells for $16 per square yard, while the latter sells for $25 per square yard (wholesale). Variable manufacturing costs are $10 per square yard and $15 per square yard for the commercial and residential grade products, respectively. On average, it takes 12 labor hours to produce 100 square yards of commercial carpeting, and 18 labor hours to produce 100 square yards of residential carpeting. The number of available labor hours at the plant is limited to 4,600 hours per week. Current sales forecasts indicate that weekly sales for the commercial line and the residential line, respectively, are 30,000 square yards and 8,000 square yards. Fixed manufacturing costs, allocated to products on the basis of 4,600 labor hours per week, amount to $1.50 and $2.25 for each square yard of commercial versus residential carpet, respectively.

Required

1. What is the gross profit (gross margin) for each of the two products, in total and per square yard?

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2. What is the contribution margin for each of the two products, in total and per square yard?

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3. Given the labor constraint and the product demand constraints, what is the optimum product mix, on a weekly basis, for each of the two products? (Show calculations.) In addition, generate a graphical solution to this problem, similar to the solution presented in Exhibit 11.21.

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4. In general, what is the rule to be followed when attempting to determine the optimum short-term product (or service) mix?

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5. What is the primary role of the management accountant in terms of addressing the short-term product-(or service-) mix problem?

EXHIBIT 11.21 Windbreakers Production and Sales Possibilities (Feasible Area) Two Production Constraints: Sewing Machine and Inspection/Packing Activity