Calculus and applications to business and economics

The demand equation for Product X is given by

P = 900/q - 0.48q + 100 q > 0
Use derivaties to explore the relationship between demand for Product X,total revenue and elasticity.

1. Find an expression for the total revenue,TR.
2. Find an expression for marginal revenue,MR.
3. Interpret the marginal revenue when q = 60.
4. What price must be charged to achieve a demand of q = 60.
5. Find an expression for dp/dq ,and evaluate at q = 60.
6. Use the relationship
dq/dp = 1/dp/dq , and the results of question (4) & (5), to determine wheather the demand is elastic,unit elastic or inelastic when q = 60 and interpret results.

7. Determine the value of q which maximises total revenue.
8. What price must be charged to maximise total revenue and verify that the demand is unit elastic at
this price.

Hints:
A. Do not attempt to obtain a equation for dq/dp in terms of p.

B. A second derivative is required in question (7)to varify a maximum.

C. Graph TR to verify algebraic answers.