Question

Formulate a linear programming problem for the following situation.

Homer Simpson has created two donut assortments for the the Springfield donut shop. The bargain assortment includes 4 pink frosted and 8 glazed donuts and the deluxe assortment contains 9 pink frosted and 3 glazed donuts. The donut shop has 300 pink frosted and 400 glazed donuts to make its assortments. Each bargain assortment makes a profit of $4 and each deluxe assortment makes a profit of $6. How many of each assortment should Homer make in order to maximize the profit?

Answer 1

If there are x bargain boxes and y deluxe boxes, you want to

maximize p = 4x + 6y where
4x+9y <= 300
8x+3y <= 400

Now use your favorite solution method or tool, and you find max p when
x=45
y=13

http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html

is a nice tool. It will solve the setup, and even graph it for you.