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A private Mom and Pops baseball company produces double aa quality baseballs and cletes. (Baseball shoes are called cletes). They have two different plants. One is in Manhattan the other in the Bronx. The one in Manhattan produces 600 double aa quality baseballs and 240 cletes an hour. The plant in the Bronx produces 240 double aa quality baseballs and 120 cletes per hour. To operate the factory in Manhattan it costs one hundred dollars per hour. Operating the factory in the Bronx is seventy five dollars per hour. Both companies must produce at least 2,520 double aa quality baseballs and 1,080 cletes each day.

a) How many hours per day should each company operate to produce the required amounts of baseballs and cletes while minimizing the cost of production?

b) What's the minimum production cost?

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The minimum production cost is clearly explored in this case.

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See the attachment please.

Formulate this as a linear programming problem.
Suppose, the plant in Manhattan operates x hours per day, and the plant in Bronx operates y hours a day.
Then, the Manhattan plant produces 600x baseballs and 240x cletes.

The Bronx plant produces 240y baseballs and 120y cletes.
The cost of operating the Manhattan plant is 100x, the cost of operating
the Bronx plant is 75y. The total cost of operation is z = 100x + 75y.
We must produce at ...

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