Chapter ISG, Problem 9.3.4P

a.

To determine

To graph $P(x)=-50000x^2+300000x-250000$ .

Answer to Problem 9.3.4P

  

Explanation of Solution

Given information:

  $P(x)=-50000x^2+300000x-250000$

Calculation:

  $P(x)=-50000x^2+300000x-250000$

Let $P(x)=y$

Table of x and y

  

The graph of $P(x)=-50000x^2+300000x-250000$

  

b.

To determine

To calculate the x -intercept.

Answer to Problem 9.3.4P

x -intercept are 1 and 5.

Explanation of Solution

Given information:

  $P(x)=-50000x^2+300000x-250000$

Calculation:

  $P(x)=-50000x^2+300000x-250000$

As Substituting $P(x)=0$in above

  $0=-50000x^2+300000x-250000$

On solving,

  $x^2-6x+5=0$

On solving,

  $x^2-5x-x+5=0$

On solving,

  $(x-5)(x-1)=0$

On solving,

x -intercept are 1 and 5.

c.

To determine

To write a equation to make profit of $150000 and solve graphically.

Answer to Problem 9.3.4P

  $x=-1$ and $x=7$

Explanation of Solution

Given information:

  $P(x)=-50000x^2+300000x-250000$

Profit $150000

Calculation:

  $P(x)=-50000x^2+300000x-250000$

Put

  $P(x)=150000$

Then

  $150000=-50000x^2+300000x-250000$

On solving,

  $50000x^2-300000x-400000=0$

On solving,

  $x^2-6x-8=0$

  

From graph approximate value

  $x=-1$ and $x=7$

d.

To determine

To calculate price of product .

Answer to Problem 9.3.4P

Product price is $\$7.47$

Explanation of Solution

Given information:

  $P(x)=-50000x^2+300000x-250000$

Profit $300000

Formula used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

  $P(x)=-50000x^2+300000x-250000$

Put

  $P(x)=300000$

Then

  $300000=-50000x^2+300000x-250000$

On solving,

  $50000x^2-300000x-550000=0$

On solving,

  $x^2-6x-11=0$

On solving,

Using formula

  $x=\frac{-(-6)\pm \sqrt{{(-6)}^2-4(1)(-11)}}{2(1)}$

On solving,

  $x=\frac{6\pm \sqrt{36+44}}{2}$

On solving,

  $x=\frac{6\pm \sqrt{80}}{2}$

On solving,

  $x=\frac{6\pm 4\sqrt{2}}{2}$

On solving,

  $\begin{array}{l}x=\frac{6+4\sqrt{2}}{2}\\ x=\frac{6-4\sqrt{2}}{2}\end{array}$

On solving,

  $x\approx -1.47$ and $x\approx 7.47$

  

Hence, product price is $\$7.47$