Posted by Ronny on Thursday, August 2, 2012 at 2:34pm.
To make pom poms in our school colors, we will have expenses of $100 to rent the Acme PomPom Plant, and then $0.25 per pom pom in materials. We believe that we can sell 500 pom poms if we charge $1.50. Assume the number sold is a linear function of the price. How much should we charge to maximize profit?
I have done this problem many times but I cannot find max profit. I keep fining a max income. I am lost and don't know what to do please help!
- Calculus Max Profit - MathMate, Friday, August 3, 2012 at 10:51am
"Assume the number sold is a linear function of the price"
but no information is given on the price elasticity, so we will assume, in general, an increase in price of $1 will increase sales by m units.
Under normal supply-demand curve, m is necessarily negative, of the order of -200 or so.
With that in mind, and knowing that (500,1.50) is a point on the line sales versus price, we construct the sales(y)-price(x) relation as:
therefore, at a price of x, we expect sales of
P=xy - cost
=xy - (0.25x+100)
=x(m(x-1.5)+500) - (0.25x+100)
To get the maximum profit, we differentiate profit with respect to price, and equate to zero to find the optimum price:
dp/dx = m*x+m*(x-1.5)+1999/4 =0
Solve for x:
If the price elasticity m=-100,
Answer This Question
More Related Questions
- POM - Acme Tire Service completed 100 tire changes, 6 brake jobs, and 16 ...
- Economics - Assume a monopolist with the following: a. Qd = 100 – 10p b. TC = 1...
- Computer Programming - I'm trying to create a vba code that solves this problem...
- business - Please check. Mary Torres owns and operates a bakery. During the past...
- Math-Algebra 2 - Ace Rent a Car charges a flat fee of $15 and $0.25 a mile for ...
- Math - How do I formulate this question to be solved in the POM-QM software? ...
- economics - 1. Assume there are three markets: A: Wool; B: Synthetic Fiber; C: ...
- Algebra 1 - For $46, Joel can rent a machine to make novelty buttons to sell at ...
- Economics - Q = 400 - 20p TC = 10 + 5q + q2 Calculate the following: Profit max ...
- ENGLISH - ive done ten sentences, five are verb and five are adjective, plese ...