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QuestionHow many microwave ovens (xx) must be produced weekly for a profit of \1250if1250 if P=\frac{1}{10}(300-x)$?

Studdy Solution

STEP 1

Assumptions1. The profit $$ is given by the formula $=\frac{1}{10} \times(300-x)$. The number of microwave ovens produced per week is $x$
3. The range of $x$ is $0 \leq x \leq200$
4. The target profit is $\$1250$

STEP 2

We are asked to find the number of ovens (xx) that must be manufactured to generate a profit of $1250\$1250. We can do this by setting the profit formula equal to $1250\$1250 and solving for xx.
110×(300−x)=1250\frac{1}{10} \times(300-x) =1250

STEP 3

To simplify the equation, we can multiply both sides by10 to get rid of the fraction.
10×110×(300−x)=10×125010 \times \frac{1}{10} \times(300-x) =10 \times1250

STEP 4

implify the equation.
300−x=12500300-x =12500

STEP 5

To isolate xx, we can subtract300 from both sides of the equation.
300−x−300=12500−300300-x-300 =12500-300

STEP 6

implify the equation.
−x=12200-x =12200

STEP 7

To solve for xx, we can multiply both sides of the equation by -1.
−1×−x=−1×12200-1 \times -x = -1 \times12200

STEP 8

implify the equation to get the solution for xx.
x=−12200x = -12200However, this solution is not valid because it falls outside the given range 0≤x≤2000 \leq x \leq200. Therefore, there is no valid solution to this problem. The manufacturer cannot generate a profit of $1250\$1250 per week with the given profit formula and production constraints.

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