Application of Algebra on Shipping Instructions

Algebra is often used to transportation were the space of the transporting vessel is a factor in order to determine shipping restrictions as a result of appropriate combinations of the goods or products to be shipped.

For instance, the figure show below for this exercise can be used to determine the number of TVs and refrigerators that can fit in an 18-wheeler truck together at any particular time.

Solution

a)	Write an inequality to describe this region. The first step is to obtain m
b)	Will the truck hold 71 refrigerators and 118 TVs?
	Substituting the number of TVs and refrigerators in the linear inequality This means that the 18-wheeler truck will not hold 71 refrigerators and 118 TVs
c)	Will the truck hold 51 refrigerators and 176 TVs?

Substituting the number of TVs and refrigerators in the linear inequality

This means that the 18-wheeler truck will not hold 176 refrigerators and 51 TVs

A linear inequality can be applied in various situations for solution where two linear inequalities exist such as a “strict” inequality and an “or equals to” inequality. This implies that a “strict” inequality is denoted by only “y or x is greater than”; whereas an “or equals to” inequality is denoted by either signs. In the case of linear inequalities, the notation for an “or equals to” inequality is a solid line; whereas the notion for a strict inequality is a dashed line. However, in order to make sure that linear inequalities are appropriately applied in solving various problems, it is necessary to determine the correct test point which is observable from the graphs plotted from the solutions of linear inequalities. A flip-flop of a plotted linear inequality within the same graph gives two parallel lines that do not intersect at any particular time.

Application of the inequality derived in the solution of problem 68 into the Burbank Buy More store, it is possible to determine the shipping restrictions between the number of TVs and refrigerators.

Therefore, in order to determine the restrictions on the graph as a result of the maximum 60 refrigerators, we must solve for x from the inequality derived in problem 68 as shown below:

Substituting the number of refrigerators in the linear inequality

Add 60 on the other side of the inequality

Then divide each side by 3 to get the value of y

This means that if a maximum of 60 refrigerators are shipped there will be no restrictions added as a result of the maximum number of TVs.

Moreover, in order to determine the restrictions on the graph as a result of the minimum 200 TVs, we must solve for y from the inequality derived in problem 68 as shown below:

Substituting the number of refrigerators in the linear inequality

This means that if 200 TVs are shipped then there will be restrictions added as a result of the maximum number of refrigerators shipped.

Reference

Dugopolski, M. (2013). Elementary and Intermediate Algebra, (4^th ed.). National American University.