The cost C of producing x number of scientic calculators is given by C = 4:50x+3

Question

The cost C of producing x number of scientic calculators is given by C = 4:50x+3000 and
the revenue R from selling them is given by R = 16:50x.
a) Find how many calculators must be sold to break even.
b) Find how much money is needed to produce the break-even number of calculators.
c) Explain in your own words what happens if a company makes and sells fewer products
than the break-even number.
d) Explain in your own words what happens if more products than the break-even number
are made and sold.

Explanation / Answer

Assuming by 4:50 you mean 4.50, and 16:50 you mean 16.50

a. In order to find how many calculators must be sold to break even, you must first set the revenue (how much you gain from selling them) equal to the cost (how much it costs to make them). Solving for x will give the number of calculators needed to have revenue equal cost.

C = 4.50x + 3000

R = 16.50x

C=R

4.50x + 3000 = 16.50x

Subtract 4.50x from both sides

3000 = 12x

Divide both sides by 12.

x = 250

b. Using the number of calculators found in the previous section, we can then plug in that quantity into the cost equation, C = 4.50x + 3000, to find the total cost of producing the calculators.

C = 4.50(250) + 3000

C = 1125 + 3000

C = 4125

c. If the company cannot sell enough calculators than the break-even number (250), then they cannot profit, because the cost to make the calculators will be greater than the revenue (profit) generated. So, over time, this company would go broke.

d. Similarly, if the company can sell more calculators than the break-even number (250), then they begin to make a profit (more revenue than cost) and they will make money (and hopefully be successful!).

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