Question

Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by

C = 70,000 + 20x
R = 300x - (x^2 / 20)
P = R - C

where production output in 1 week is x calculators. If production is increasing at a rate of 600 calculators per week when production output is 5,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit.

Answer 1

just plug and chug:

dC/dt = 20 dx/dt = 20*600
dR/dt = 300 dx/dt - x/10 dx/dt = (300-500)(600)
dP/dt = dR/dt - dC/dt