Answer:
$6.00
Explanation:
Given data
quantity demanded ( x )  ∝ 1 / p^3       for p > 1 
when p = $10/unit , x = 64 
initial cost = $140, cost per unit = $4
<u>Determine the price that will yield a maximum profit </u>
x = k/p^3 ----- ( 1 ).  when x = 64 , p = $10 , k = constant 
64 = k/10^3 
k = 64 * ( 10^3 ) 
   = 64000 
back to equation 1 
x = 64000 / p^3 
∴ p = 40 / ∛x
next calculate the value of revenue generated 
Revenue(Rx) = P(price ) * x ( quantity )
                = 40 / ∛x * x   =  40 x^2/3 
next calculate Total cost of product 
C(x) = 140 + 4x 
Maximum Profit  generated = R(x) - C(x) = 0 
                                               = 40x^2/3 - 140 + 4x  = 0 
                                               =  40(2/3) x^(2/3 -1) - 0 - 4 = 0
                                             ∴ ∛x = 20/3    ∴     x = (20/3 ) ^3 = 296
profit is maximum at x(quantity demanded ) = 296 units 
hence the price that will yield a maximum profit 
P = 40 / ∛x
   = ( 40 / (20/3) )  = $6