Question 1: 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 per glove are given in the following table.
|
Model
|
Production Time (hours)
|
Profit/Glove
|
|
Cutting
and Sewing
|
Finishing
|
Packaging
and Shipping
|
|
Regular Model
|
1
|
0.5
|
0.125
|
$5
|
|
Catcher's model
|
1.5
|
0.33
|
0.25
|
$8
|
|
Capacity available
|
900
|
300
|
100
|
|
The company is interested in maximizing the total profit, formulate a linear programming model for this problem and solve it using Excel?
Question 2: The Water Sports Company soon will be producing and marketing a new model line of motor boats. The production manager, Michael Jensen, now is facing a make-or-buy decision regarding the outboard motor to be installed on each of these boats. Based on the total cost involved, should the motors be produced internally or purchased from a vendor? Producing them internally would require an investment of $1 million in new facilities as well as a production cost of $1,600 for each motor produced. If purchased from a vendor instead, the price would be $2,000 per motor.
Michael has obtained a preliminary forecast from the company's marketing division that 3,000 boats in this model line will be sold.
a) Use spreadsheets to display and analyze Michael's two options. Which option should be chosen?
b) Michael realizes from past experience that preliminary sales forecasts are quite unreliable, so he wants to check on whether his decision might change if a more careful forecast differed significantly from the preliminary forecast. Determine a break-even point for the production and sales volume below which the buy option is better and above which the make option is better.
Question 3: The Move-It Company has two plants building forklift trucks that then are shipped to three distribution centers during a given month. The production costs are the same at the two plants, and the cost of shipping each truck is shown below for each combination of plant and distribution center:
|
Plant
|
Distribution Center
|
|
1
|
2
|
3
|
|
A
|
$800
|
$700
|
$400
|
|
B
|
$600
|
$800
|
$500
|
Each plant can produce a total of 30 forklift trucks per week. Each distribution center must receive exactly 20 trucks per week.
Management's objective is to determine how many forklift trucks should be shipped from each plant to minimize total shipping cost. Formulate and solve an LP model for this problem using Excel and find the total cost.