Thank you A large company in the communication and publishing industry has quant

Question

Thank you A large company in the communication and publishing industry has quantified the relationship between the price or one or ns products and the demand for this product as Price = 160-0.01 times Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) - $52,000 and the variable cost per unit $45. What is the maximum profit that can be achieved if the maximum expected demand is 6.000 units per year? What is the unit price at this point of optimal demand?

Explanation / Answer

P=160-0.01Q

Total revenue=PQ=160Q-0.01Q2

Fixed cost=52000

Variable cost=45Q

Total cost=45Q+52000

Profit(P)=Total revenue-total cost

       =160Q-0.01Q2-45Q-52000

dP/dQ=160-0.02Q - 45 =0

Q=5750<6000

P=160-0.01(5750)=102.5 $

     

   

       

       

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