Amanufacturer sells each of his tv sets for $85. the cost c (in dollars) of manufacturing and selling x tv sets per week is c = 1500 + 10x + 0.005x2. if at most 10,000 sets can be produced per week, how many sets should be made and sold to maximize the weekly profit?

7500 sets

Step-by-step explanation:

We are given that

Cost of each TV set=$85

The cost C(in dollars) of manufacturing  and selling x Tv sets per week is given by

Set can be produced at most per week=10000

We have to find the number of sets should be made and sold to maximize the weekly profit.

Revenue=85 x

Where x= number of sets selling per set

Profit=Revenue-Cost

Profit=85x-(1500+10x+0.005x^2)[/tex]

Profit=P=

Differentiate w.r.t x

Substitute

Again differentiate w.r.t x

Hence,function is maximize.

Therefore, 7500 sets should be made and sold to maximize the weekly profit.

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