# MATH

Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is \$3.50, and the profit for each model B grate is \$4.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day.

Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
x,y=
What is the optimal profit?

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1. What are the constraints?
x+y >= 150
x >= 0
y >= 0
3x + 4y <= 1000
6x + 3y <= 20*60
You want to maximize
p = 3.50x + 4.00y

So now solve in the usual way. Graph the region and evaluate p(x,y) at each vertex. There are several good linear algebra calculator web sites online.

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