Question

• c(x) = 1.5 the steps of an employees calculation for the profit, p(x), are given below. why is the final equation incorrect? use the drop - down menus to explain your answer. p(x)=s(x)·n(x)-c(x)·n(x) step 1: p(x)=x(3,000 - 500x)-1.5(3,000 - 500x) step 2: p(x)=3,000x - 500x²-1.5(3,000 - 500x) step 3: p(x)=3,000x - 500x²-4,500 - 750x step 4: p(x)=-4,500 + 2,250x - 500x² click the arrows to choose an answer from each menu. the first error in the employees calculation occurred in step choose... in that step, choose... the correct final equation for the profit function should be p(x)= choose...

Explanation:

Step1: Identify error location

Check sign in Step3 expansion.

Step2: Expand $-1.5(3000-500x)$

$$\begin{align*} -1.5(3000-500x) &= -1.5\times3000 + (-1.5)\times(-500x)\\ &= -4500 + 750x \end{align*}$$

Step3: Combine like terms

$$\begin{align*} P(x) &= 3000x - 500x^2 - 4500 + 750x\\ &= -500x^2 + (3000x+750x) -4500\\ &= -500x^2 + 3750x -4500 \end{align*}$$

Answer:

The first error in the employee's calculation occurred in Step 3.
In that step, the employee incorrectly calculated $-1.5(-500x)$ as $-750x$ instead of $+750x$.
The correct final equation for the profit function should be $P(x) = -500x^2 + 3750x - 4500$