Your company would like to know how sales levels affect profits. If too few item

Question

Your company would like to know how sales levels affect profits. If too few items are sold, then there is a loss. Even if too many items are sold, however, the company can lose money (likely because of low pricing). It is good to know how many items can be sold for there to be profit.

Functions are very useful in many areas, such as in business to find the profit an organization is making. For example, the following function expresses profit in terms of the number of phones sold by a particular company:

P(x) = –x2 + 110x – 1,000

This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smartphones.

1. Compute the following: P(5), P(50), and P(120). Then, interpret the results.

Can you show me how to compute the -x^2 in all 3. 

Explanation / Answer

P(5)= -(25)+550-1000= Loss in Profits...$-475 P(50)=-(2500)+5500-1000= Gain...$2000 P(120)=-(144000)+132000-1000= Loss...$-2200 Max Profits: 55 sold... thus.. as you reach the number 55 in products sold, the Profits will increase, after this number, the profits will go down until 100 products are sold.. which would be $0 in profits. Thus, in order for the store to make the most money, their goal should be around the maximum profit area. More than 100 products sold would cause the store to lose money.

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