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Problem 14

Describe the three steps in solving a linear programming problem.

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The three steps in solving a linear programming problem are as follows:
Step 1: Formulate the Linear Programming Problem, which involves identifying the objective function, decision variables, and linear constraints. The objective function represents what we aim to maximize or minimize, the decision variables are the unknowns that influence the objective function, and the linear constraints represent the restrictions of the problem.
Step 2: Graph the Feasible Region by plotting the linear constraints on a coordinate plane. The feasible region is the area where all constraints are satisfied simultaneously. This region holds all potential solutions.
Step 3: Identify the Optimal Solution within the feasible region. For maximization problems, find the point(s) in the region where the objective function has the highest value. For minimization problems, seek the point(s) where the objective function has the lowest value. These points are the optimal solutions. Even though, sometimes, there can exist multiple optimal solutions or no solution at all based on the specifics of the feasible region and the problem.

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Chapter 11

Susan Smith manages the Wexford plant of Sanchez Manufacturing. A representative of Darnell Engineering approaches Smith about replacing a large piece of manufacturing equipment that Sanchez uses in its process with a more efficient model. While the representative made some compelling arguments in favor of replacing the 3 -year-old equipment, Smith is hesitant. Smith is hoping to be promoted next year to manager of the larger Detroit plant, and she knows that the accrual-basis net operating income of the Wexford plant will be evaluated closely as part of the promotion decision. The following information is available concerning the equipment replacement decision: Sanchez uses straight-line depreciation on all equipment. Annual depreciation expense for the old machine is \(\$ 180,000\) and will be \(\$ 270,000\) on the new machine if it is acquired. For simplicity, ignore income taxes and the time value of money. 1\. Assume that Smith's priority is to receive the promotion and she makes the equipment-replacement decision based on the next one year's accrual-based net operating income. Which alternative would she choose? Show your calculations. 2\. What are the relevant factors in the decision? Which alternative is in the best interest of the company over the next 2 years? Show your calculations. 3\. At what cost would Smith be willing to purchase the new equipment? Explain.

Chapter 11

Define relevant costs. Why are historical costs irrelevant?

Chapter 11

Wechsler Company produces three products: \(A 130, B 324,\) and C587. All three products use the same direct material, Brac. Unit data for the three products are: The demand for the products far exceeds the direct materials available to produce the products. Brac costs S9 per pound, and a maximum of 5,000 pounds is available each month. Wechsler must produce a minimum of 200 units of each product. 1\. How many units of product \(A 130, B 324\), and \(C 587\) should Wechsler produce? 2\. What is the maximum amount Wechsler would be willing to pay for another 1,200 pounds of Brac?

Chapter 11

How might the optimal solution of a linear programming problem be determined?

Chapter 11

Lees Corp. is deciding whether to keep or drop a small segment of its business. Key information regarding the segment includes: Contribution margin: 35,000 Avoidable fixed costs: 30,000 Unavoidable fixed costs: 25,000 Given the information above, Lees should: a. Drop the segment because the contribution margin is less than total fixed costs. b. Drop the segment because avoidable fixed costs exceed unavoidable fixed costs. c. Keep the segment because the contribution margin exceeds avoidable fixed costs. d. Keep the segment because the contribution margin exceeds unavoidable fixed costs.

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