Chapter MPS, Problem 6.1MPS

(a)

To determine

To Find: The polynomial of the product.

Answer to Problem 6.1MPS

  $-0.001x^2+5x-500$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Cost of product sellling }x\text{ units}=0.001x^2+5x+500\\ \text{Revenue from selling }x\text{ units}=10x\end{array}$

Formula Used:

  $\text{Profit}=\text{Revenue}-\text{Cost of gross selling of product}$

Calculation:

  $\begin{array}{l}=10x-\left(0.001x^2+5x+500\right)\\ =-0.001x^2+5x-500\\ x=1850\end{array}$

Conclusion:

Thus the polynomial is $-0.001x^2+5x-500$ .

(b)

To determine

To Find: the profit from the sales of product.

Answer to Problem 6.1MPS

  $5327.5$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Cost of product sellling }x\text{ units}=0.001x^2+5x+500\\ \text{Revenue from selling }x\text{ units}=10x\end{array}$

Formula Used:

  $\text{Profit}=\text{Revenue}-\text{Cost of gross selling of product}$

Calculation:

  $\begin{array}{l}=10x-\left(0.001x^2+5x+500\right)\\ =-0.001x^2+5x-500\\ x=1850\\ \text{profit}=-0.001{\left(1850\right)}^2+5\times 1850-500\\ =-3422.5+9250-500\\ =5327.5\end{array}$

Conclusion:

Thus the profit is $5327.5$ .