Marginal cost of violins

Question

The annual demand equation for handcrafted violins by a certain violin maker can be approximated by p=24-x where p is the price in thousands of dollars and x is the quantity of violins demanded. Find and interpret the marginal revenue for each of the given production levels. A.) x=5 b.) x=10 c.) x=12

Answer 1

R(x) = revenue if x violins are produced and sold

 

       = (price per violin in thousands of $)(number of violins)

 

       = x(24-x) 

 

       = -x²+24x

 

Marginal revenue = change in revenue caused by a one unit increase in                               the level of production

 

Marginal revenue when x = 5:  R(6) - R(5) = 108 - 95 = 13

 

   If the level of production is increased from 5 violins to 6 violins, we expect that the total revenue from the sale of all 6 violins will increase by $13,000 from what the revenue was when 5 violins were produced and sold.  

 

Do the other two parts in a similar manner.   

Answer 2

p=24-5=$19,000

 

p=24-10= $14,000

 

p=24-12 = $12,000