I am the project director for a company that manufactures and sells Hoover Boards. Over the past fifteen years, the marketing research department for my company has established the following information.
The cost of producing x items is based on a fixed cost of $1600 and a variable cost of $1500 per x items per week. The price-demand function has been determined to be p = 1600 x . −
There has been a great deal of discussion here on what we should be looking at to set guidelines for prices. We would like you to develop a function that describes Cost, Revenue and Profit based on this data. In an effort to be efficient, we need you to find the break-even point to the nearest whole unit, find the profit function and where we will have a profit of 0. Also, could you possibly find how to maximize the profit to the nearest thousand dollars?
To help you accomplish these tasks, we suggest that you follow the following steps:
1. Find the Cost Function
2. Find the revenue function
3. Find the Break Even Point. Where the Cost = Revenue
4. Find the Profit function. Profit = Revenue – Cost.
5. Find where the Profit will equal zero.
6. Find where the profit will be at a maximum and what the maximum profit will be.
We look forward to your final technical memo. We expect that the report will include all necessary work and calculations. A scientific expert (your instructor) is available to answer any questions that you might have in the course of your investigation.
C = Fixed cost + Variable cost⋅x R = x p⋅
R = C
P = R C−
P = 0
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