Imagine you are the owner and the CEO of a small company manufacturing specialty kayaks. You have designed a new kayak and are trying to analyze the costs, the revenues, the profits associated with the productions and sales of this new product. You have determined that you will have to spend $150,000 on the new production line set-up and the advertising, and that after that it will cost you $400 to produce each kayak. You also conducted market research which showed that the demand equation for the new kayak is (p+10q=3000) where q is the number of the kayaks that will be purchased at the price p dollars per kayak. You decided that you will always price the kayaks at the highest price at which all manufactured kayaks will be sold. Now, do the following analysis. Required:
a. Express the company’s costs C that will be incurred in the production of the new kayak, the revenue R and the profit P from the sales of the kayak as functions of the quantity q of these kayaks that are manufactured and sold.
b. Determine what levels of production will result in the company breaking even.
c. Determine what levels of production will lead to the company making as large profit as possible, what is the maximum possible profit that the company can make by manufacturing and selling the new kayak.
d. Determine what level of production will result in the company’s revenue being as large as possible.