Question

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Model Cutting and Sewing Finishing Packaging and Shipping Profit/Glove Regular model 1 1/2 1/8 $5 Catcher's model 3/2 1/3 1/4 $8 Assuming that the company is interested in maximizing the total profit contribution, answer the following:

a. What is the linear programming model for this problem?

b. Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture? (PLEASE POST A CLEAR GRAPH, PREFERIBLE ONE MADE ON THE COMPUTER)

c. What is the total profit contribution Kelson can earn with the given production quantities? d. How many hours of production time will be scheduled in each department? e. What is the slack time in each department?

Answer 1

Consider the provide details to solve the subparts.

a.According to the provided details, the Kelson Sporting Equipment Inc. makes two types of baseball gloves, a regular model and a catcher model. Consider R are the number of units of regular model and C are the number of units of catcher model. The cutting and the sewing department have total 900 hours production time available to produce two types of baseball gloves, so the constraint for the cutting and the sewing department is given as:

Similarly, the finishing department have total 300 hours production time available to produce two types of baseball gloves, so the constraint for the finishing department is given as:

Similarly, the packaging and Shipping department have total 100 hours production time available to produce two types of baseball gloves, so the constraint for the packaging and shipping department is given as:

And the profit obtained from the regular model is $5 and the profit obtained from the Catcher model is $8, hence the total maximum profit contribution from two types of gloves is:

Hence, the linear programming model for to maximize the profit contribution from two types of gloves is given as:

Subject to the constraints:

And the non-negative constraints is given as:

b.

Enter the above obtained linear programming model in the Excel spreadsheet, the screenshot of the model is shown below:

Now introduce the decision variables, in the cell C12 and D12, calculate the total time used for each of the department by using the SUMPRODUCT function and calculate the total profit in the cell C19 by using the SUMPRODUCT function, the screenshot of the formula is shown below:

Now, click on the “Data” tab in the menu bar, and press the “Solver option” a new dialog box will appear. Set the objective as “Max” and fill the cell C19, in the changing cell option select the cell C12:D12. Press on the “add” button to add the constraint for the time used for the three different department, the screenshot is shown below:

Now, press “ADD” button in the above dialog box, and add the non-negativity constraint, the screenshot is shown below:

Press “OK” option in the above dialog box, the screenshot is shown below:

Select the Solving method as “Simplex”. And press the solve button in the above dialog box. The screenshot of the obtained output is shown below:

Hence, there should be 500 regular model and 150 Catchers model for each keelson manufacture.

c.According to the above output, the total profit contribution Kelson can earn with the optimal production quantities.

d.According to the above output, the hours of production time for cutting and sewing department is 725 hours, the hours of production time for finishing department is 300hours and the hours of production time for packaging and Shipping department is 100 hours.

e.According to the above output, the slack time for cutting and sewing department is 175 hours, the slack time for finishing department is 0 hours and the slack time for packaging and shipping department is 0 hours.