Kane Manufacturing has a division that produces two models of hibachis, model A

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 Bhibachi requires 7 lb of cast iron and 6 min of labor. The profit for each model A hibachi is $5, and the profit for each model B hibachi is $4.50. 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?What is the largest profit the company can realize?

Explanation / Answer

Model A 6lb and 12 min profit $5

Model B 7 lb and 6 min Profit $4.5

2200 lb and 40 min

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 =

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