Tricky Math Problem

Question

Suppose the cost function for purchasing "Zombie Death Bats" (patent pending) in quantities, q, is given by the equation C(q) = 2000 + 3,650/q + q/28 

What quantity will minimize the cost? 

Answer 1

To minimize a function, take the derivative and set it equal to zero. Then solve for "q".

For C(q) = 2000 + 3,650/q + q/28 or

C(q) = 2000 + 3,650q^-1 + q/28 then

dC/dq = C'(q) = -3650q^-2 + 1/28 = 1/28 - 3650/q²

Setting this equal to zero we get:

1/28 - 3650/q² = 0

1/28 = 3650/q²

q²/28 = 3650

q² = 28•3650

q² = 102200

q = √102200 = 319.687 ≈ 320