Problema Solution
Chasity runs a factory that makes stereo tuners. Each R80 takes 9 ounces of plastic and 3 ounces of metal. Each G150 requires 3 ounces of plastic and 9 ounces of metal. The factory has 264 ounces of plastic, 360 ounces of metal available, with a maximum of 24 R80 that can be built each week. If each R80 generates $11 in profit, and each G150 generates $14, how many of each of the stereo tuners should Chasity have the factory make each week to make the most profit?
Answer provided by our tutors
let
x = the number of R80 made
y = the number of G150 made
the plastic used for making x + y stereo tuners is
9x + 3y <= 264
the metal used for making x + y stereo tuners is
3x + 9y <= 360
maximum of 24 R80 can be built each week
x <= 24
the factory want to make maximum profit, we need to find the maximum value of P(x, y) = 11x + 14y
Draw the graph of
9x + 3y <= 264
3x + 9y <= 360
x <= 24
and find the corner points and plug them into P(x, y) = 11x + 14y to find the maximum value
(18, 34)
P(18 , 34) = 11*18 + 14*34 = 674
(24, 16)
P(24, 16) = 11*24 + 14*16 = 488
(24, 32)
P(24, 32) = 11*24 + 14*32 = 712
P(x, y) has the biggest value for x = 24 and y = 32 thus to make the most profit the factory should make 24 R80 stereos and 32 G150 stereos.