Kelson Sporting Equipment, Inc. , makes two different types of baseball gloves:
ID: 2647350 • Letter: K
Question
Kelson Sporting Equipment, Inc. , makes two different types of baseball gloves: a regular model and a catchers 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 (in minute) requirements and the profit contribution per glove are given in the following table:
A) What is the maximized profit the company can make?
B) Which constraints are binding?
C) If one-hour overtime can be scheduled in just one of the departments, which department would you recommend doing so?
Model Cutting & Sewing Finishing Packaging Profit/Glove Regular model 1 1/2 1/8 $5 Catcher's model 3/2 1/3 1/4 $8Explanation / Answer
Working Note:
(1) Maximum production with given number of hours:
(a) Cutting & Sewing:
Regular = 1 x 900 x 60 = 54,000, Or
Catchers' = (3/2) x 900 x 60 = 81,000
(b) Finishing
Regular = 2 x 300 x 60 = 36,000, Or
Catchers' = 3 x 300 x 60 = 54,000
(c) Packaging
Regular = 8 x 100 x 60 = 48,000, Or
Catchers' = 4 x 100 x 60 = 24,000
(A) Since each unit passes through all 3 departments, we can see that maximum number of Regular gloves that can be produced is [Min (54000, 36000, 48000]) = 36,000 gloves.
Corresponding profit = 36,000 x $5 = $180,000
Maximum number of Catchers' gloves that can be produced is [Min (81000, 54000, 24000)] = 24,000 gloves.
Corresponding profit = 24,000 x $8 = $192,000
So, Maximized profit is $192,000.
(B) The binding constraint is Number of hours available in each department.
(C) I would recommend that the additional hour be provided in Packaging, because more number of Catchers' gloves can be produced (using all 3 departments) if number of units made in Packaging department (which now has the lowest output) increases.
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