Question

The cost, in millions of dollars, of building a three-story high school in new york state was estimated to be?

Answer 1

The answer is 18.33 thousand square feet.

The total revenue will be $\ 0.23$ million times the number of thousands of square feet. Therefore the revenue function will be, $R(x)=0.23 x$

Now, profit is revenue minus the total costs. Therefore the profit function can be found by subtracting the cost function from the revenue function.

$\begin{aligned}&P(x)=R(x)-C(x)=0.23 x-\left(1.5+0.15 x-0.0001 x^{2}\right) \\&=0.0001 x^{2}+0.08 x-1.5\end{aligned}$

The break-even point is where the profit is zero, i.e., there is neither a profit nor a loss.

$\begin{aligned}&0.0001 x^{2}+0.08 x-1.5=0 \\&x=\frac{-0.8 \pm \sqrt{0.08^{2}+4 *(0.0001) * 1.5}}{2 * 0.0001} \\&x=18.33 \quad x=-818.33\end{aligned}$

So to find the size of the school that is the break-even point we equate the profit function to zero and solve for $\mathrm{x}$. To break-even, the size of the school should be 18.33 thousand square feet.

What is Profit Function?

• Subtracting the cost function from the revenue function yields the profit function.
• As a result, in this question, we will start with the revenue function. The break-even point may be determined after the profit function is provided.

To learn more about Profit Function visit:

https://brainly.com/question/16866047

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