Suppose the Total Cost of producing x pair of shoes is represented by

Question

Suppose the Total Cost of producing x pair of shoes is represented by 

 .

Determine the cost of producing 62, 65, 66, and fixed cost.

a) The total cost of producing 62 pair of shoes: Incorrect 

b) The total cost of producing 65 pair of shoes: Incorrect  

c) The total cost of producing 66 pair of shoes:  

d) What is the fixed cost of producing shoes?

Answer 1

C(x) = 1.3x^3 + 7.3x^2 - 0.7x + 137

C(62) = 1.3(62)^3 + 7.3(62)^2 - 0.7(62) + 137

= 309826.4 + 28061.2 - 43.4 +137

= 338,068 for 62 shoes; 5452.7 per one pair of shoes

C(65) = 1.3(65)^3 + 7.3(65)^2 -0.7(65) + 137

= 357012.5 + 30842.5 + 45.5 = 388,037.5 for 65 shoes; 5,969.8 per one pair of shoe

C(66) = 1.3(66)^3 + 7.3(66)^2 - 0.7(66) + 137

= 373744.8 + 31798.8 + 46.2 +137 = 405726.8 for 66 shoes;

6147.4 per shoe pair. the 66th shoe pair cost 405726.8 - 388037.5 = 17,689.3

Fixed Cost =C(0) = 137

C'(x) = 3.9x^2 + 14.6x - 0.7 = 0

x= -14.6/7.8 + or - (1/7.8)sqr(14.6^2 + 4(3.9)(.7))

= about 0.43

C(.43) = 1.3(.43)^3 + 7.3(.43)^2 -0.7(.43) + 137 = minimum cost at 0.43 shoes

=.103 + 1.35 - .301 +137 = 138,754 for .43 shoe pair, less than one shoe

cost per shoe pair = 138.754/.43 = 322.68 = minimum cost for a shoe pair

if Cost is measured in cents, maybe the numbers make sense.