Chapter 7.4, Problem 45E

Solution

The correction option for the solution of the system of inequality.

  $\begin{array}{l}\text{Objective function: }f=5x+10y\\ \text{Constraints:}\left\{\begin{array}{l}2x+y\le 10\\ x+3y\le 12\\ x\ge 0,y\ge 0\end{array}\right.\end{array}$

A. $\left(0,0\right)$

B. $\left(5,0\right)$

C. $\left(0,4\right)$

D. $\left(3,4\right)$

E. $\left(3.6,2.8\right)$

The correct choice is D.

Given Information:

The system of inequality is defined as,

  $\begin{array}{l}\text{Objective function: }f=5x+10y\\ \text{Constraints:}\left\{\begin{array}{l}2x+y\le 10\\ x+3y\le 12\\ x\ge 0,y\ge 0\end{array}\right.\end{array}$

Explanation:

Consider the given inequality,

  $\begin{array}{l}\text{Objective function: }f=5x+10y\\ \text{Constraints:}\left\{\begin{array}{l}2x+y\le 10\\ x+3y\le 12\\ x\ge 0,y\ge 0\end{array}\right.\end{array}$

Draw the inequality by using the graphing calculator.

  

Compare the obtained point over the graph from all the options given in the question.

The only point $\left(3,4\right)$ is not the boundary point in the above graph.

Hence, the required correct option is D.