2) A certain company does research and believes that thequantity, Q, that will be demanded by consumers is related to theprice by the function ?(?) = 25000 − 320?2.

a) Find a formula for revenue, R(p). Then use your formula tofind the total revenue when selling the items at $1.50 each, andfind the total revenue when selling the items at $8.50 each. Showyour work.

b) Use the revenue function and calculus to solve for the pricethat creates the highest revenue.
Show all work/clearly explain all steps to use calculus to solvethe problem. You can use Excel to solve the equation, but you mustclearly show what equation is being solved and explain yourprocess. Write a complete sentence to explain what your answertells us about the revenue.

c) Find a formula for elasticity of demand E(p). Then use yourformula to find the elasticity when
the price of each item is $1.50, and find the elasticity when theprice of each item is $8.50. Show your work. Then write a completesentence to interpret the meaning in context including anexplanation of whether or not it is elastic or inelastic at eachprice as well as whether or not they should or should not raise theprice.

d) Use the elasticity function to solve for when the priceelasticity of demand is equal to −1. Show the equation you aresolving. You can solve the equation using Excel or you can solve byhand. Write a complete sentence to explain what your answer tellsus about the revenue.

e) What do you notice about your answers to part ii) and partiv)? Write a short paragraph describing two methods that can beused to solve for the maximum revenue if we have a revenuefunction.