Question

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula P = 1 /10 x (300 − x) provided that 0 ≤ x ≤ 200. How many ovens must be manufactured in a given week to generate a profit of $1610?

Answer 1

Answer:

Number of ovens must be manufactured in a given week to generate a profit of $1610  is 70

Step-by-step explanation:

We are given

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula

$P=\frac{1}{10}x(300-x)$

provided that 0 ≤ x ≤ 200

We are given

profit is $1610

so, we can set P=1610

and then we can solve for x

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

now, we can factor it

$(x-70)(x-230)=0$

we can solve for x

and we get

$x=70,x=230$

Since, x=230 does not lie on 0 ≤ x ≤ 200

So, we will consider only x=70

So,

Number of ovens must be manufactured in a given week to generate a profit of $1610  is 70