Question

A manufacturer of headphones is preparing to set the price on a new design. Demand is thought to depend on the price and is represented by the model D=2,500 – 3P The accounting department estimates that the total costs can be represented by C = 5,000+5D

Answer 1

Given Headphone Manufacturing Informations

• Demand = 2500-3P
• Total Cost = 5000+5D

Q1: Which is the correct model for the total revenue TR in terms of the price, P

Total Revenue(TR) = Price of Unit x Units Sold

Price of Unit = P, Units Sold is the demand of the Headphone

                           TR =  P x (2500-3P)

                           TR = 2500P-3P²
Total Revenue (TR) in terms of the price, P is 2500P-3P²

Q2: Which is the correct model for the total cost TC in terms of the price, P

Total Cost = 5000+5D

Putting the value of D for converting TC in terms of the Price(P)

TC = 5000+5D

      = 5000+5( 2500-3P)

       = 5000 + 12,500-15P

       = 17,500 - 15P

Total Cost (TC) in terms of the price, P = 17,500 - 15P

Q3: Which is the correct model for the total profit TP in terms of the price, P

Total Profit = Total Revue - Total Cost                 
Putting the value of TR and TC in formulae.
Total Profit = TR-TC
Total Profit= (2500-P) - (17,500 - 15P)

Total Profit (TP) in terms of the price, P is (2500-P) - (17,500 - 15P)

All the very best, take care