Question

Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model A hibachi requires 6 lb of cast iron and 12 min of labor. To produce each model B hibachi requires 7 lb of cast iron and 6 min of labor. The profit for each model A hibachi is $8, and the profit for each model B hibachi is $7.50. If 2200 lb of cast iron and 40 labor-hours are available for the production of hibachis each week, how many hibachis of each model should the division produce each week to maximize Kane's profit?

Model A hibachis?
Model B hibachis?
What is the largest profit the company can realize?
Is there any raw material left over?

Answer 1

6a + 7b <= 2200 pound iron
12a + 6b <=2400 minutes labor

graph those (a on x and b on y)
line 1 (iron)
(367,0) and (0,314) solution on or below)
line 2 (labor)
(200,0) and (0,400) (solution on or below)
intersection at (75,250)
so test 3 points
(0,314)
(75,250)
(200,0)
with profit = 8x + 7.5 y
point 1
p = 8(0) + 7.5*314 = $2355
point 2
p = 8(75)+7.5(250) = $ 2475 winner
point 3
p = 8(200) +7.5(0) = $1600
point 1 p =