Question

A pen manufacture company introduces production bonus to the workers that increases the cost of pens. the daily cost of production C for y pens is given by c(y)=(2.05y+550)rupees.find if it is known that atleast 500 pens can be sold daily,what price the company should charge per piece to guarantee no ...

Answer 1

Given:

A pen manufacture company introduces a production bonus to the workers that increase the cost of pens.

the daily cost of production C for y pens is given by C(y) = (2.05y+550) rupees

To find:

Find if it is known that at least 500 pens can be sold daily, what price the company should charge per piece to guarantee no loss

Solution:

It is given,

"C" → the daily cost of production

"y" → no. of pens

Fuction ⇒ C(y) = (2.05y + 550)

We have,

The no. of pens sold per day = 500

So, we will substitute the value of y = 500 in the given function to find the daily cost of production,

$C(500) = (2.05 \times 500) + 550$

$\implies C(500) = 1025 + 550$

$\implies \bold{C(500) = Rs.\:1575}$ ← the daily cost of production for 500 pens

Now,

If the daily cost of production for 500 pens is = Rs. 1575

Then, the daily cost of production for 1 pen is = $\frac{1575}{500} = \bold{Rs. \:3.15}$

Thus, the manufacturing company should charge Rs. 3.15 for each piece of 500 pens to guarantee no loss.

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