Chapter 6.3, Problem 32PPS

a.

To determine

To write: The equations to represent the situation.

Answer to Problem 32PPS

  $y=60x+16000$ and $y=80x+12000$ .

Explanation of Solution

Let x represents the units shipped and y represents the total cost for x units.

For factory A, the equation becomes:

  $\begin{array}{c}\left(y-39160\right)=\frac{41260-39160}{421-386}\left(x-386\right)\\ y-39160=60(x-386)\\ y=60x+16000\end{array}$

For factory B, the equation becomes:

  $\begin{array}{c}\left(y-45200\right)=\frac{52160-45200}{502-415}\left(x-415\right)\\ y-45200=80(x-415)\\ y=80x+12000\end{array}$

So, the system of equations becomes:

  $y=60x+16000$ and $y=80x+12000$ .

b.

To determine

To find: The solution of the system by using elimination.

Answer to Problem 32PPS

  $x=200,y=28000$

Explanation of Solution

The system of equations is

  $y=60x+16000$ ......... (1)

  $y=80x+12000$ ......... (2)

Subtract equation (1) from equation (2) to eliminate y.

  $\begin{array}{c}y-y=\left(80x+12000\right)-\left(60x+16000\right)\\ 0=20x-4000\\ x=200\end{array}$

Now, substitute $x=200$ in equation (1) to find the value of y.

  $\begin{array}{c}y=60\left(200\right)+16000\\ =12000+16000\\ =28000\end{array}$

So, the solution of the system is $x=200,y=28000$ .

c.

To determine

To explain: the meaning of the solution obtained in part (b).

Explanation of Solution

The solution of the system is given by $x=200,y=28000$ . That means, each factory will have the same cost of $28000 for 200 units shipped.