3. Telson Sporting Inc., makes three different types of baseball
gloves: a regular model,

a catcher’s model, and a premium model. Each month, the firm has
267.25 hours of

production time available in its cutting department, 85.5 hours
available in its finishing

department, and 143 hours available in its packaging department.
The production time

(in hours) requirements per glove are given in the following
table:

……………………Cutting Finishing Packaging

Regular Model……… 1…… 1/2 ……….2/5

Catcher’s Model …5/3 …….1/4 ……….4/5

Premium Model… 5/4 ……..1/5………. 3/4

Telson Sporting Inc. sells regular model $9.6 per glove,
catcher’s model $12.7 per glove,

and premium model $14.1 per glove. On the other hand, a regular
model uses $1.4 worth

of raw materials and $0.3 worth of shipping cost per glove, a
catcher’s model uses $2.3

worth of raw materials and $0.4 worth of shipping cost per
glove, and a premium model

uses $3.1 worth of raw materials and $0.5 worth of shipping cost
per glove.

Demand for regular and catcher’s models are unlimited, but at
most 117 units of premium

models can be manufactured each month.

a) Formulate a linear programming model that can be used to
determine the number of

units of each model that should be produced in order to maximize
Telson Sporting Inc.’s

profit (Write the complete model for the problem. Make sure to
give clear definitions

of your decision variables).

b) Solve the problem by using Excel Solver (Hand-in both the
value and formulas printouts

for the problem). Show the optimal solution and optimal value in
your printouts.