Problema Solution
Rosalyn works no more than 20 hours a week during the school year. She is paid $10 an hour for tutoring geometry students and $7 an hour for delivering pizzas for Pizza King. She wants to spend at least 3 hours but no more than 8 hours a week tutoring. Find Rosalyn’s maximum earnings.
Answer provided by our tutors
let
x = the number of hours tutoring per week, x>0
y = the number of hours delivering pizza per week, y>0
Rosalyn works no more than 20 hours a week during the school year:
x + y <= 20
x >=3
x <= 8
the formula describing the earnings per week is:
F(x, y) = 10x + 7y
First we will graph the following system of equalities to find the corner points:
x + y <= 20
x >=3
x <= 8
y >= 0
click here to see the graph:
the corner points are:
(3, 17), (8, 12)(3, 0)(8, 0)
the value of F(x, y) in the corner points is:
F(3, 17) = 10*3 + 7*17 = $149
F(8, 12) = 10*8 + 7*12 = $164
F(3, 0) = 10*3 = $30
F(8, 0) = 10*8 = $80
Rosalyn’s maximum earnings are $164.