2) A certain company does research and believes that the quantity, Q, that will be demanded...

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

a) Find a formula for revenue, R(p). Then use your formula to find the total revenue when selling the items at $1.50 each, and find the total revenue when selling the items at $8.50 each. Show your work.

b) Use the revenue function and calculus to solve for the price that creates the highest revenue.
Show all work/clearly explain all steps to use calculus to solve the problem. You can use Excel to solve the equation, but you must clearly show what equation is being solved and explain your process. Write a complete sentence to explain what your answer tells us about the revenue.

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

d) Use the elasticity function to solve for when the price elasticity of demand is equal to −1. Show the equation you are solving. You can solve the equation using Excel or you can solve by hand. Write a complete sentence to explain what your answer tells us about the revenue.

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

Expert Solution

milcah answered 2 years ago

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