Question

Raw material and manufacturing cost of a product is 10$. If selling price of one unit
of the product is x$, and the number of units sold N is given by formula below.
Compute the optimal price that maximizes the profit.
N =9/x-10
+ 12(100 - x)​

Answer 1

Answer:

$100 \times 100 = 200$

Answer 2

Step-by-step explanation:

Selling price of 1 item =Rs.(330−x)(Given)

Selling price of x items =Rs.x(330−x)

Cost price of x items =Rs.(x

2

+10x−12)

Profit = Selling price − Cost price

⇒ Profit =(330x−x

2

)−(x

2

+10x−12)

=320x−2x

2

+12

Now,

P=−2x

2

+320x+12

Differentiating above equation, we get

dx

dP

=−4x+320

Differentiating againg w.r.t. x, we get

dx

2

d

2

P

=−4⇒ Always negative

To maximize the profit,

dx

dp

=0

−4x+320=0

x=

−4

−320

=80

∵

dx

2

d

2

P

<0 for any value of x, thus 80 items must be sold so that his profit is maximum.