   # Taylor Company produces two industrial cleansers that use the same liquid chemical input: Pocolimpio and Maslimpio. Pocolimpio uses two quarts of the chemical for every unit produced, and Maslimpio uses five quarts. Currently, Taylor has 6,000 quarts of the material in inventory. All of the material is imported. For the coming year, Taylor plans to import 6,000 quarts to produce 1,000 units of Pocolimpio and 2,000 units of Maslimpio. The detail of each product’s unit contribution margin is as follows: Taylor Company has received word that the source of the material has been shut down by embargo. Consequently, the company will not be able to import the 6,000 quarts it planned to use in the coming year’s production. There is no other source of the material. Required: 1. Compute the total contribution margin that the company would earn if it could import the 6,000 quarts of the material. 2. Determine the optimal usage of the company’s inventory of 6,000 quarts of the material. Compute the total contribution margin for the product mix that you recommend. 3. Assume that Pocolimpio uses three direct labor hours for every unit produced and that Maslimpio uses two hours. A total of 6,000 direct labor hours is available for the coming year. a. Formulate the linear programming problem faced by Taylor Company. To do so, you must derive mathematical expressions for the objective function and for the materials and labor constraints. b. Solve the linear programming problem using the graphical approach. c. Compute the total contribution margin produced by the optimal mix. ### Cornerstones of Cost Management (C...

4th Edition
Don R. Hansen + 1 other
Publisher: Cengage Learning
ISBN: 9781305970663

#### Solutions

Chapter
Section ### Cornerstones of Cost Management (C...

4th Edition
Don R. Hansen + 1 other
Publisher: Cengage Learning
ISBN: 9781305970663
Chapter 20, Problem 25P
Textbook Problem
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## Taylor Company produces two industrial cleansers that use the same liquid chemical input: Pocolimpio and Maslimpio. Pocolimpio uses two quarts of the chemical for every unit produced, and Maslimpio uses five quarts. Currently, Taylor has 6,000 quarts of the material in inventory. All of the material is imported. For the coming year, Taylor plans to import 6,000 quarts to produce 1,000 units of Pocolimpio and 2,000 units of Maslimpio. The detail of each product’s unit contribution margin is as follows: Taylor Company has received word that the source of the material has been shut down by embargo. Consequently, the company will not be able to import the 6,000 quarts it planned to use in the coming year’s production. There is no other source of the material.Required: 1. Compute the total contribution margin that the company would earn if it could import the 6,000 quarts of the material. 2. Determine the optimal usage of the company’s inventory of 6,000 quarts of the material. Compute the total contribution margin for the product mix that you recommend. 3. Assume that Pocolimpio uses three direct labor hours for every unit produced and that Maslimpio uses two hours. A total of 6,000 direct labor hours is available for the coming year. a. Formulate the linear programming problem faced by Taylor Company. To do so, you must derive mathematical expressions for the objective function and for the materials and labor constraints. b. Solve the linear programming problem using the graphical approach. c. Compute the total contribution margin produced by the optimal mix.

1.

To determine

Calculate the total contribution margin of the company.

### Explanation of Solution

Contribution margin: Contribution margin is a measurement of performance where only revenue and variable costs are taken into consideration. Hence, this measurement is useful in the evaluation of the probable outcomes of decisions including pricing decisions and other marketing strategies that affect primarily revenue and variable costs.

Calculate the total contribution margin of the company as follows:

Total contribution margin = (Contribution margin of Product P+Contribution margin of Product M

2.

To determine

Compute the optimal usage for each product and calculate the total contribution margin for the product mix.

3. a.

To determine

Construct the mathematical expression for the object function, material and labor.

3. b.

To determine

Solve the linear programming under the graphical approach.

3. c.

To determine

Calculate the total contribution margin produced by the optimal mix.

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