Rate of Change In Cost

Question

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given byC=80000+40x, R=200−x/240,where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:

Rate of change in cost = 

Rate of change in revenue = 

Rate of change in profit = 

Answer 1

Rate of change of cost = dC/dt = 40dx/dt = 40(500) = 20000 $/wk

Rate of change of revenue = dR/dt = -dx/dt/240 = -500/240 = -2.983 $/wk (with -x²/40 --> -2x/40 dx/dt)

Rate of (P = R - C ) dP/dt = dR/dt-dC/dt from linearity property of derivatives.

The revenue function doesn't seem to have the right scale, and the form is odd as well. (Something like 200000 - x²/40, for example would be more reasonable)