Chapter 6.3, Problem 71HP

(a)

To determine

To Find: The graph of the given function.

Answer to Problem 71HP

The required graph is shown in Figure 1.

Explanation of Solution

Given:

The given function is $40t+25c=1500$ .

Calculation:

Consider the given function is,

  $40t+25c=1500$

The graph of the above function is shown in Figure 1

  

Figure 1

(b)

To determine

To Find:Thegraph for the equation to represent this situation on the same graph as the one in part (a).

Explanation of Solution

Consider that the company always produces two chair with the table. The required expression is,

  $\begin{array}{l}2t=c\\ t=0.5c\end{array}$

The graph for the above function is shown in Figure 2

  

Figure 2

(c)

To determine

To Find:The number of tables and the chairs that the company can produce each week.

Answer to Problem 71HP

The number of table is 16 and the chair is 32.

Explanation of Solution

Consider the expressions,

  $\begin{array}{l}40t+25c=1500\\ c=2t\end{array}$

Then,

  $\begin{array}{l}40t+25\left(2t\right)=1500\\ t=\frac{1500}{90}\\ t=16\end{array}$

Then, the number of chairs is,

  $2\left(16\right)=32$

Thus, the number of table is 16 and the chair is 32.

(d)

To determine

To Find: The way to determine the answer with the graph.

Answer to Problem 71HP

The intersection of the two graphs of Figure 1 and Figure 2 shows the number of the table and chairs that is produced in each week.

Explanation of Solution

Consider that the number of chair and the table is determined by the graph shown in Figure 1 and the two. The intersection of the two graphs and the intersection point shows the number of the tables and the chairs that can be produced in each week.