Let C be the function whose graph is given below. This graph represents the cost

Question

Let C be the function whose graph is given below. This graph represents the cost C of manufacturing q computers in a day. Use it to answer parts a-f. 100, 280 000) 50,000 00,000 150,000 100,000 50,000 (50, 51 000) Number of computers a. Determine the cost of manufacturing no computers in a day; that is, determine C(0). Interpret the meaning of this value b. Determine the number of computers needed to be manufactured in order to have a cost of $32,000 per day. Approximate the number of computers needed to be manufactured in order to have a cost of $200, 000 per day. c. d. For what values ofq will the cost be between $19,000 and $51,000 per day? Use interval notation e. What is the domain of the function? What does this imply in terms of the daily production? f. Give an explanation as to why the domain for this function is not all real numbers.

Explanation / Answer

Solution -

a) From graph we can see point is (0,5000)

So C(0) =5000

Here 5000 is operating cost.

b) From graph we can find point

(30, 32000)

So 30 computers needed to manufactured

c) From graph we can find point (100, 200000)

So 100 computers needed to manufactured

D) We have two points on graph (10,19000) and (50 , 51000)

So If interval for q is (10,50) , cost will be between 19000 to 51000

E) Here Domain is [0,100]

It means company can make minimum 0 and maximum 100 computers .

F) Domain is not all real numbers because number of computers can not be negative .

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