A company makes two kinds of tires: Model r and model s. Each tire is processed on three machines: A, b, c. To make one model r requires 1/2 hour o machine a, 2 hours on machine b, and 1 hour on c. To make one models requires 1 hour on a, 1 hour on b and 4 hours on c. During the next week machine a will be available for at most 20hours, machine b for at most 60 hours, and machine c for at most 60 hours. If the company makes a $10 profit on each model r tire and $15 profit on each model s tire, about how many of each tire should be made to maximize the company's profit? What would the profit be?

Given:
tire= r s
machines ABC

r= 1/2*A=2B=1C

s= 1*A=1B=4C

A->20h
B->60h
c->60h

r= +10$
s= +15$

Max use of Machines based off their most efficient usage:
A(20)=20*2*r=40*10

B(60)=60s=60*15

C(60)=60r=60*10

Total Profits:
40*10+60*10+60*15
=100*10+60*15
=1000+60*10+60*5
=1000+600+300
=1900$