c(x)=0.005x^3+0.07^2+18x+700

Question

What is the current monthly​ cost?
​b)	What would be the additional cost of increasing production to 83 chairs​ monthly?
​c)	What is the marginal cost when x=80​?
​d)	Use the marginal cost to estimate the difference in cost between producing 80 and 82 chairs per month.
​e)	Use the answer from part​ (d) to predict ​C(82​).

Answer 1

a) Assume current production is 80: c(80)=5148 monthly cost.

b) c(83)-c(80)=387.165 or 387.17 additional cost.

c) c(81)=5274.475, so marginal cost is 5274.475-5148=126.48.

If, however, we use calculus to calculate the rate of change, we differentiate: c'(x)=0.015x²+0.14x+18 and put x=80. This gives us 125.20 instead of 126.48.

d) If the marginal cost at x=80 is 126.475, then at x=82 the additional cost would be twice this at 252.95. If we use the calculus figure the additional cost would be 250.40.

e) Prediction for c(82)=5148+252.95=5400.95, or 5148+250.40=5398.40 if we use the calculus figure.

My guess is that you’re supposed to use the non-calculus figure (precalculus method).