Answer to Question #96179 in Algebra for Rohma Mazhar

Question

suppose you decided to buy a toy factory. From financial statements of the toy-factory you have estimated a cost to produce x toys: C(x) = 50x - 20000. The scale price for each toy is $11. You also have found that the maximum capacity of the production of the company is 1200 toys a month.

(a) analyze the data and determine what it will take to break even, and decide whether to buy this toy-factory or not.

Answer 1

Cost function:$C(x)=50 x-20,000$ .

Selling price of each toy$=11$ .

Let the factory manufactures $x$ toys per month. The net profit(always greater than zero) may be written as:

$P=11x-(50x-20000)=20000-39x>0,$

$x<\frac{20000}{39}=512.82,$

which means buying that factory is only beneficial if the factory produce toys less than 512 in a month.

The profit function also states that the profit of the factory decreases as the number of toys manufactured increases and it can have maximum profit (20,000) when it does not produce even a single toy.

So, buying this factory is not feasible as profit of the factory decreases as the number of toys manufactured increases.