Suppose the variable cost v of producing q pairs of shoes by hand from a local c

Question

Suppose the variable cost v of producing q pairs of shoes by hand from a local cobbler is defined in the following way:

For less than 5 pairs of shoes, the variable cost is cq2 + 8q since the cobbler makes each by hand alone. For quantities at q=5 pairs and beyond, the cobbler hires friends to help, and thus the variable cost is q3 cq

This information gives the following piecewise function given below. For what value of the constant c is this function continuous on its domain [0, )?

v(q) =  

(sorry this formatted weird)

Explanation / Answer

v = cq^2 + 8q ; 0 <= q < 5
v = q^3 - cq ; q >= 5

Clearly the transition value is q = 5

Plug in q = 5 and equate em together :
c(5)^2 + 8(5) = (5)^3 - c(5)
25c + 40 = 125 - 5c
30c = 125 - 40
30c = 85
c = 85/30
c = 17/6 ---> ANS

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