Target Shirt Company Makes Three Varieties of Shirts: Collegiate,Traditional and European.These

question 26

Essay

Target Shirt Company makes three varieties of shirts: Collegiate,Traditional and European.These shirts are made from different combinations of cotton and polyester.
The cost per yard of unblended cotton is $5 and for unblended polyester is $4.Target can receive up to 4,000 yards of raw cotton and 3,000 yards of raw polyester fabric weekly.The table below pertinent data concerning the manufacture of the shirts. $\begin{array}{c}\begin{array}{c}\\\underline{\text {Shirt}}\\\text {Coll egiate}\\\\\text {Traditional}\\\\\text {European}\\\\\end{array}\begin{array}{c}\text {Total}\\\text {Yards}\\1.00\\\\1.20\\\\.90\\\\\end{array}\begin{array}{c}\text {Fabric}\\\underline{\text{Requirement}}\\\text {At least}\\\text { 50 \% cotton}\\\text {No more than}\\\text { 20 \% polyester}\\\text {As much as}\\\text {80 \% polyester}\end{array}\begin{array}{c}\text{Weekly}\\\underline{\text{Contracts}}\\500\\\\650\\\\280\\\\\end{array}\begin{array}{c}\text {Weekly}\\\underline{\text {Demand}}\\600\\\\850\\\\675\\\\\end{array}\begin{array}{c}\text {Selling}\\\underline{\text {Price}}\\\$14.00\\\\ \$ 15.00 \\\\\$ 18.00 \\\\\end{array}\end{array}$
Formulate and solve this blending problem as a linear program.

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Definitions:

Machine-hour

A measure of production time, calculated as the total hours a machine is operated within a specific period.

Maintenance Cost

The expense associated with the upkeep and repair of equipment or facilities, ensuring they continue to operate efficiently.

Independent Variable

A variable in an experiment or model that is manipulated or changed to observe its effect on a dependent variable.

Overhead Cost

Indirect costs not directly tied to production but necessary for running business operations, such as rent, utilities, and administrative expenses.