Question

eBook 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) Cutting and Packaging and Model Sewing Finishing Shipping Regular model 1 1/2 1/8 Catcher's model 3/2 1/3 1/4 Profit/Glove 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? Enter the answers as fractions or round the answers to 3 decimal places. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0" Let R = number of units of regular model. C = number of units of catcher's model. Max 5 OR + 8 s.t.

Answer 1

The above problem is formulated as below:

	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
Hour available	900	300	100

Let R units of Regular and C units of Catcher's model be made

Total profit = 5R + 8C
Subject to
R + 3/2C <= 900		Cutting and Sewing
1/2R + 1/3C <= 300	Finishing
1/8R + 1/4C <= 100	Packaging and Shipping
R,C>=0

The same is formulated in excel as given below:

A B C D E H 1 2 3 Cutting and Sewing Finishing Packaging and Shipping 1/8 Profit/ glove 5 1 $5 Regular model Catcher's model Hour available 3/2 1/2 1/3 300 1/4 $8 900 100 7 8 R. 9 10 11 13 12 13 14 Let R units of Regular and C units of Catcher's model be made Total profit = 5R + 8C Subject to R + 3/2C<= 900 Cutting and Sewing 1/2R + 1/3C <= 300 Finishing 1/8R + 1/4C <= 100 Packaging and Shipping R,C>=0 15 î û Ñ 900 300 100 16 17

The formulation in solver is done as shown below:

Solver Parameters Х Set Objective: $G$12 To: бMax O Min O Value Of: By Changing Variable Cells: $D$10:$E$10 Subject to the Constraints: Add Change $D$10 = integer $D$10 >= 0 $E$10 = integer $E$10 >= 0 $G$14 <= $1$14 $G$15 <= $1$15 $G$16 <= $1$16 Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

The solver solution is given below:

A B C D E F G H I 2 3 Finishing Profit/ glove 4 Cutting and Sewing 1 3/2 900 Packaging and Shipping 1/8 1/4 5 1/2 $5 6 Regular model Catcher's model Hour available $8 1/3 300 100 9 10 11 12 3700 13 RC 500 150 Let R units of Regular and C units of Catcher's model be made Total profit = 5R + 8C Subject to R + 3/2C<= 900 Cutting and Sewing 725 1/2R + 1/3C <= 300 Finishing 300 1/8R + 1/4C <= 100 Packaging and Shipping 100 R,C>=0 û 14 15 îi î 900 300 100 16 17

a. Max 5R + 8C

Subject to

R + 3/2C <= 900

1/2R + 1/3C <= 300

1/8R + 1/4C <= 100

R,C>=0

b. From the excel snapshot above,

Regular model = 500 units

Catcher's model = 150 units

c. Total profit = $3700

d. Cutting and sewing - 725 hrs

Finishing - 300 hrs

Packaging and Shipping - 100 hrs

e. Slack time in each dept:

Cutting and sewing: Available hrs - utilized hrs = 900 - 725 = 175 hrs

Finishing = 300-300 = 0

Packaging and Shipping = 100-100 = 0 hrs

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