# LINR 3 | Lesson 2 | Try This! (Writing the Inequality) Solutions

## Writing the Inequality

Writing the Inequalities

• Let $$x$$ represent the number of phones with the least features and $$y$$ represent the number of phones with the most features.
• Orange: $$x+y \leq 25$$ represents the combinations of each type of phone that can be produced within the 25 phone limit.
• Green: $$2x+4y\leq80$$ represent the combinations of the two types of phones that use 80 hours of labor.
• Note:  There can not be a negative number of phones; therefore:
• $$x \geq 0$$
• $$y \geq 0$$

Information about the points should include the following:

• The point $$(40,0)$$ represents the maximum number of phones with the most features that can be manufactured in the allotted $$80$$ hours $$= 40$$.
• The point $$(0,20)$$ represents the maximum number of phones with the most features that can be manufactured in 80 hours if no phones with the least features are produced.
• $$(25,0)$$ and $$(0,25)$$ are the maximum number of phones with the least features and phones with the most features that can be produced given the plant limitations.
• $$(10,15)$$ represents the maximum number of each phone that can be produced that uses all the plant capacity and the labor hours available (10 phones with least features and 15 phones with the most features can be produced while maximizing both the time and capacity constraints). 