A producer finds that demand for his commodity obeys a linear demand equation p+4x=10, where p is in dollars and x in thousands of units. If the cost equation is C(x)=3.2x^2+0x+1.25 what price should be charged to maximize the profit?
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We have demand function
Thus revenue function R(x) is
We have cost function `C(x)=3.2x^2+0x+1.25`
Thus profit function is
differentiate P(x),with respect to x
`P'(x)=10-7.2xx2 xx x`
For maximum profit, P'(x)=0
Thus x=10/14.4 ,will give maximum profit
We have given demand function
Revenue function R(x) is
`cost function `
Thus profit is
differentiate with respect to p ,we have
For maximum profit ,P'=0
P''=(1/4)(-3.6) <0 for all p.
Thus P=7.22 $ will provide maximum profit.
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