Question

A company manufactures cassettes. Its cost and revenue functions are C(x)=26000+30xand R(x)=43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?

Answer 1

For this we just need to find the break even point.

Lets try for x = 1000,
C(1000) = 26000+30000=56000 & R(1000)=43000; this shows loss

Lets try for x = 2000,
C(2000) = 26000+60000=86000 & R(2000)=86000; this shows the break even point

This mean that in order to get any profit cassettes in access of 2000 need to be produced per week.

Answer 2

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Given that,

Cost, C(x) = 20 x + 4000

Revenue, R(x) = 60x + 2000

We know that, profit = Revenue – Cost

Now, subsitute the given data in the above formula,

Profit = R(x) – C(x)

Profit = (60x + 2000)-(20 x + 4000)

Now, simplify it:

Profit = 60x + 2000 -20x -4000

Profit = 40x – 2000

To earn some profit, 40x – 2000 > 0

⇒40x > 2000

⇒ x>2000/40

⇒ x > 50

Thus, the manufacturer should sell more than 50 items to realise some profit

Hope it's Helpful....:)