Posted by **Amber** on Saturday, May 7, 2011 at 4:49pm.

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.

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?

$

- finite math -
**Damon**, Saturday, May 7, 2011 at 5:32pm
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 =

- finite math -
**Amber**, Saturday, May 7, 2011 at 6:00pm
thanks sooooo much!

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