Question

A company discovers that to produce x=870 new electronic parts, it will cost y=$89,170. To produce 860 new electronic parts, it will cost $88,260.Compute the slope of the costs and choose the most accurate statement from the following:

Costs are decreasing at a rate of $91 per item.
Costs are decreasing at a rate of $87 per item.
Costs are increasing at a rate of $87 per item.
Costs are decreasing at a rate of $85 per item.
Costs are increasing at a rate of $85 per item.
Costs are increasing at a rate of $91 per item.

Answer 1

The slope of the cost function is calculated as $91, which indicates that costs are increasing at a rate of $91 per electronic part.

Step-by-step explanation:

To compute the slope of the cost function, which represents the rate of change of cost with respect to the number of items produced, we use the formula for slope (m) given by the difference in y-values divided by the difference in x-values. In this case:

m = (y2 - y1) / (x2 - x1)

For the two given points (x1, y1) = (870, 89170) and (x2, y2) = (860, 88260), we find the slope as follows:

m = (88260 - 89170) / (860 - 870)

m = (-910) / (-10)

m = 91

Since the slope is positive, it indicates that costs are increasing at a rate of $91 per item. Therefore, the most accurate statement is "Costs are increasing at a rate of $91 per item."