Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model-A hibachi requires 3 lb of cast iron and 6 min of labor. To produce each model-B hibachi requires 4 lb of cast iron and 3 min of labor. The profit for each model-A hibachi is $2, and the profit for each model-B hibachi is $1.50. There are 1000 lb of cast iron and 19 labor-hours available for the production of hibachis each day.

Question

How many hibachis of each model should the division produce to maximize Kane's profit?
model A ___ hibachis
model B ___ hibachis

What is the largest profit the company can realize?
$

Answer 1

Now this is a linear programming problem (not the same chapter as the other ones you asked)

make a of A and b of B
constraints
3a+4b </= 1000 pounds iron
6a+3b </= 19*60 or 1140 minutes labor
graph those (a on x and b on y)
line 1 (iron)
(333,0) and (0,250) solution on or below)
line 2 (labor)
(190,0) and (0,380) (solution on or below)
intersection at (104,172)
so test 3 points
(0,250)
(104,172)
(190,0)
with profit = 2 x+1.5 y
point 1
p = 2(0) + 1.5*250 = $375
point 2
p = 2(104)+1.5(172) = $ 466 winner
point 3
p = 2(190) +1.5(0) = $380
point 1 p =

Answer 2

thanks sooooo much!