Question

A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon is given by Upper C prime (x )equalsnegative 0.00001 x squared minus 0.02 x plus 58 for x less than or equals 1600​, where Upper C prime (x )is in cents. Approximate the total cost of manufacturing 1600 yards of​ ribbon, using 5 subintervals over [0 comma 1600 ]and the left endpoint of each subinterval.

Answer 1

$624.90

Explanation:

The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.

The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)

The estimated cost is ...

320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents

≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon