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# Linear Programming to Maximize Contribution Margin

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Find the optimal quantities to produce for product X, Y, and Z and the necessary quantities of labor and material

Products
X Y Z
Labor Hrs 5 4 2
Material A lbs. 2 2 .5
Material B lbs 1 0 2

-I'm given a budget of \$11,980 for production of the three products. Currently, the company has a contractual obligation for at least 85 units of product Y per week to one of its major customers.

-In order to produce its products, the company needs two materials, material A and B.
-Material A costs \$4 per pound, as does material B. Labor costs \$8 per hour.
-Product X sells for \$122 a unit, product Y sells for \$115 per unit, and product Z sells for \$76 a unit.

I like to know the quantity of each product to be produced, how much labor will be needed and the amount of each material to purchase to maximize contribution margins.

Linear Programming problem