A cleaning service cleans homes. For each house call, the cost to the company is

Question

A cleaning service cleans homes. For each house call, the cost to the company is approximately $40 for cleaning supplies, gasoline, and labor. The business also has fixed monthly costs of $300 from phone service, advertising, and depreciation on the vehicles. write a cost function to represent the cost C (x) for x house calls per month. Write the average cost function that represents the average cost Cas)for x boise calis per tnont. Evaluate Cang(5), cing(0)%,Joo), cavg(100). The eleaning service can realistically make a maximum of 160 calls por month. However, if the number of calls were unlimited, what value would the average cost approach? What does this mean in the context of the problem? o o ?o

Explanation / Answer

For each house call, the cost to the cleaning service company is $ 40 towards cleaning supplies, gasoline and labor. In addition, there are fixed costs of $ 300 per month towards phone service, advertising and depreciation on vehicles.

If x house calls are made in a month, then the variable cost is $ 40x . Also, considering the fixed monthly costs, we have C(x) = 40x+300.

The average cost function is given by Cavg(x) = total cost/no. of house calls = (40x+300)/x.

We have Cavg(5) =(40*5+300)/5 = 500/5 = $100, Cavg(20) = (40*20+300)/20 = 1100/20= $55, Cavg(30) =(40*30+300)/30 = 1500/30= $ 50 and Cavg(100) =(40*100+300)/100 = 4300/100 = $ 43.

We have Cavg(x) =(40x+300)/x = 40+300/x. Thus, if x becomes larger and larger, approaching infinity, then 300/x approaches 0 so that , in such a case, Cavg(x) approaches $ 40. In the context of the problem, it means that the average cost per month per house call, will become close to the variable cost per house call, if the number of such calls increase indefinitely.

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