Question

6x² + c 60x A company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is C'(x) = where x is the number of units produced (a) Find the cost function, given that the company incurs a fixed cost of $15,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $19,000 to produce 5 units. Should they seek this new source? (a) What substitution should be used to determine the cost function? Use the quantity as the substitution, us so that du = O dx The cost function is C(x)= (b) Therefore, the cost of producing 5 units is so the company seek a new source of investment income (Round to the nearest dollar as needed.)

Answer 1

-242)2 (a) The marginal cost function is given by c'ex) = 6ox cwith cro) = 15 6xte Integrating on both sides Sc'ex) dx 60X 6xte S S Cox) = Gox da exte use the quantity 6x te as the substitution u=6xte so that du = 12x da 5 du Cx) = scoa da = 5inku)/+c, 6xte Replace u= 68 te we get the cost function C(x) = 5 In 1 (6x te) ltci Use CCO) -15 S CCO) = 5 ini coco+e))+c, 15 = 5 Inleltc, since inced=1 15 =5+, » c = 10 5 Thus, the cost function is ccx) = 5 In 16* tel + 10 (b) when x=5 we have C(5) - = 5In16 (5) tel+10 = 5 In/150 tel + 10 235.143 This means the cost is about $35, 143 Therefore, the cost of producing 5 units is 8 35,143 so the company should seek the new source of investment income.