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? 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 R + C s.t. R + C - Select your answer -≤≥=Item 5 Cutting and Sewing R + C - Select your answer -≤≥=Item 9 Finishing R + C - Select your answer -≤≥=Item 13 Packing and Shipping R, C - Select your answer -≤≥=Item 15
(b)	Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture?
	Regular Model =  units
	Catcher's Model =  units
(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?
	Department Time Used (Hours) Cutting and Sewing Finishing Packing and Shipping
(e)	What is the slack time in each department? If your answer is zero, enter “0”.
	Department Slack Time (Hours) Cutting and Sewing Finishing Packing and Shipping

Answer 1

Answer:

(a), (b), (c), (d)

Packaging Profit = 1/2 А Model Cutting Finishing Regular =1/2 =1/8 Catcher =3/2 =1/4 Decision Variables Number of units of each model of glove Model No.of units Regular Catcher Objective function Maximize the profit 11 =SUMPRODUCT(B7:38,E2:E3) 12 Constraints 13 =SUMPRODUCT(B7:38,B2:B3) 14 =SUMPRODUCT(B7:38,C2:03) 300 15 =SUMPRODUCT(B7:38,02:03) 200 16 17 900 W W

A 2 3 7 B C D E Model Cutting Finishing Packaging| Profit Regular 0.5 0.13 1 15.00 Catcher 1.50 0.25 0 .50 7.00 Decision Variables Number of units of each model of glove Model No.of units Regular Catcher Objective function Maximize the profit 0 Constraints 0 900 300 200 8 10

Gevuldpriy- Solver Parameters Set Objective: SA$11 To: Max Min value of: By Changing Variable Cells: $B$7:$B$8 Subject to the Constraints: SA$13:$A$15 <= $C$13:$C$15 SB$7:SBS8 = integer $B$7:$B$8 >= 0 Add Change 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

A B C D E Model Cutting Finishing Packaging Profit Regular 0.5 0.13 1 5 .00 Catcher 1.50 0.250.50 7.00 Decision Variables Number of units of each model of glove Model No.of units Regular 0 Catcher 400 Objective function Maximize the profit 2800 Constraints 600 900 100 300 200 200

(e)

Slack time for cutting = 900-600 = 300 hours

Slack time for finishin = 300-100 = 200 hours

Slack time for packaging = 200-200 = 0 hours