Problema Solution
A studio sells photographs and prints. it costs $50 to purchase each photograph and it take 4 hours to frame it, It costs $100 to purchase each print and it take 5 hours to frame it. The store has at most $1800 to spend it and at most 120 hours to frame. It makes $60 profit on each photo. and $100 profit on each print. find the number of each that the studio should purchase to maximize profits.
Answer provided by our tutors
let
x = the number of purchased photographs, x>=0
y = the number of purchased prints, y>=0
First we will find the constrains:
50x + 100y <=1800
4x + 5y <= 120
The objective function is:
F(x, y) = 60x + 100y
We try to find the maximum of the function by drawing:
50x + 100y <=1800
4x + 5y <= 120
to find the corner points
the corner points are: (30, 0), (0, 18) and (20, 8)
F(30, 0) = 60*30 + 100*0 = $1,800
F(0, 18) = 60*0 + 100*18 = $1,800
F(20, 8) = 60*20 + 100*8 = $2,000
the maximize the profit the studio should purchase 20 photographs and 8 prints.