Bill's Sporting Goods makes baseballs and softballs. In a given week they can manufacture no more than 70 balls. When setting equipment, they have to make at least 20 baseballs and at least 10 softballs. They make 6$ for each softball sold and 5$ for each baseball sold. What is Bill's maximum profit in a week from the sale of baseballs/softballs?
maximize p
p = 6s+5b
s+b</=70
b>/=20
s>/=10
sketch a graph
there are two intersections to check
(s,b) = (10,60)
here p= 60+300 = 360
and
(s,b) = (50 ,20)
here p=300 + 100 = 400 (winner)