G:dollars to manufacture x units of a device in an hour at one of their manufacturing centers. How many devices should be manufactured each hour to minimize average cost? .002x+160 units What is the resulting average cost of a device? $ How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ.

- How many devices should be manufactured each hour to minimize average cost? **21000** units.

- What is the resulting average cost of a device? $ 441160.001

- How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ. $ 0.00

The marginal cost and the average cost are absolutely the same at the optimal cost.

Explanation:

C(x) = 441000 + 160x + 0.001x²

Average cost = (Total cost)/(number of units)

Average cost = (441000/x) + 160 + 0.001x

At minimum average cost,

dAC/dx = 0 (Note: AC means average cost)

dAC/dx = - 441000/x² + 0.001

when it is equal to 0

- 441000/x² = - 0.001

x² = 441000/0.01 = 441000000

x = 21000 units

Average cost of a device.

Average cost = (441000/x) + 160 + 0.001x

For one device, x = 1

average cost = (441000/1) + 160 + 0.001(1)

Average cost of a device = 441000 + 160 + 0.001 = $ 441160.001

At optimal level, that is, x = 21000 units

Average cost = (441000/x) + 160 + 0.001x = (441000/21000) + 160 + 0.001(21000) = $202

Marginal cost = dC/dx (Rate of change of total cost with the number of units)

C(x) = 441000 + 160x + 0.001x²

Marginal cost = (dC/dx) = 160 + 0.002x

At x = 21000 units

Marginal cost = 160 + 0.002(21000) = $202

The marginal cost and the average cost are absolutely the same at the optimal cost.

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.

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