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, 240 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 packaging
model and sewing finishing and shipping profit/glove
regular model 1 1/2 1/8 $8
catcher's model 3/2 1/3 1/2 $4
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 your answer is zero, enter "0". if you need a negative number, enter minus sign with it. if necessary, enter the numbers as a common fraction. if the constant is "1" it must be entered in the box.
let r = number of units of regular model.
c = number of units of catcher's model.
max r + c
s. t.
r + c ≤ cutting and sewing
r + c ≤ finishing
r + c ≤ packaging and shipping
r, c ≥
b. what is the total profit contribution kelson can earn with the given production quantities? if required, round your answer to the nearest dollar.
c. how many hours of production time will be scheduled in each department? if required, round your answer to the nearest whole number.
c & s
f
p & s
c. what is the slack time in each department? if required, round your answer to the nearest whole number. if no entry is required, enter "0".
department capacity usage slack
c & s hours
f hours
p & s hours