The cost in dollars to produce X designer dog leashes is C(x)=4x+8 and the price demand function in dollars per leash is p(x)=116-4x find the revenue function R(x)

984

Step-by-step explanation:

The Profit function is the revenue minus the cost.

Revenue = Price x Quantity =  X.px = x(116-4x) = 116x - 4

Therefore the profit function P (x):  

P (x)  =  116x - 4 - (4x+8)

P (x)   = -4 +112x -8

To maximise profit we use the 1st order condition: dP(x)/dq = 0

Therefore,  112 - 8x = 0

8x = 112

x =14

So 14 leashes maximises profit.

The revenue is: -4()+112*14 -8 = 984

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