The cost, in dollars, to produce x designer dog leashes is C ( x ) = 8 x + 3 , and the price-demand function, in dollars per leash, is p ( x ) = 88 − 2 x Find the profit function. P ( x ) = Find the number of leashes which need to be sold to maximize the profit. Find the maximum profit. Find the price to charge per leash to maximize profit. What would be the best reasons to either pay or not pay that much for a leash?

Profit maximising price = 48

Explanation:

Total Cost : C (x) = 8x + 3

Demand Curve : p (x) = 88 − 2x

Total Revenue = p (x). x  =  x (88 - 2x) = 88x - 2x^2

Profit maximisation is where Marginal Cost (MC) = Marginal Revenue (MR)

MC = d TC / d Q  =   d (8x + 3) / d x = 8

MR = d TR / d Q = d (88x - 2x^2) / d x = 88 - 4x

Equating MR & MC ,

88 - 4x = 8  , 88 - 8 = 4x

x = 80 / 4 , x = 20

Putting value in demand curve,

p = 88 - 2x = 88 - 2 (20) = 88 - 40

p = 48

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