Manufacturing A factory manufactures two products, each requiring the use of three machines. The first machine can be used at most 70 hours; the second machine at most 40 hours; and the third machine at most 90 hours. The first product requires 2 hours on machine 1, 1 hour on machine 2 and 1 hour on machine 3 the second product requires 1 hour each on machines 1 and 2 and 2 hours on machine 3 If the profit is $35 per unit for the first product and $60 per unit for the second product, how many units of each product should be manufactured to maximize profit?

Question

Manufacturing A factory manufactures two products, each requiring the use of three machines. The first machine can be used at most 70 hours; the second machine at most 40 hours; and the third machine at most 90 hours. The first product requires 2 hours on machine 1,   1 hour on machine 2 and 1 hour on machine 3 the second product requires  1 hour each on machines 1 and 2 and 2 hours on machine 3 If the profit is $35 per unit for the first product and $60 per unit for the second product, how many units of each product should be manufactured to maximize profit?

Steve · Answer

If the 3 products are made in quantities x,y,z, then

maximize p=35x+60y subject to
2x+y <= 70
x+y <= 40
x+2y <= 90

maximum profit at (0,40) = 2400

good tool at

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

set the x- and y- ranges at 0-50 and it will show a decent graph of the region.