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 200 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
1/2
1/8
1
$5
Catcher's model
3/2
1/4
1/2
$7
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? If
required, round your answers to 3 decimal places or enter your
answers as a fraction. 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? If
your answer is zero enter “0”.
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? If required, round your answer to one decimal
place.
Department
Production Time (Hours)
Cutting and Sewing
Finishing
Packing and Shipping
(e)
What is the slack time in each department? If your answer is
zero, enter “0”. If required, round your answer to one decimal
place.
Department
Slack Time (Hours)
Cutting and Sewing
Finishing
Packing and Shipping