Answer and Explanation:
Given:
Total car = 200
Rate = $29
Computation:
Total increase in rate = a
So , Total decrees in car = 5a
Total income (y) = [200-5a][29+a]
y = 5,800 + 200a - 145a - 5a²
y = 5,800 + 55a - 5a²
y' = dy / da [5,800 + 55a - 5a²]
y' = -10a + 55
in which , y' = 0
0 = -10a + 55
a = 5.5
So , Maximum rate = $ [29+5.5]
Maximum rate = $34.5
maximum income = 5,800 + 55(5.5)- 5(5.5)²
maximum income = 5,800 + 302.5 - 151.25
maximum income = $5951.25
