# Math Help - Linear Programming - Inequalities help

1. ## Linear Programming - Inequalities help

You have a sweet tooth and have a craving for Silky bars and Munchie crunch. You have $20 in your pocket, Silky Bars -$2 and Muinchie Crunch - $2.50. When you get to the shop you find that there are only 5 Silky Bars left. How do you write down the contraints as a system of inequalities? 2. Hello, pozmans! You have a sweet tooth and have a craving for Silky Bars and Munchie Crunch. You have$20 in your pocket.
Silky Bars cost $2 each and Munchie Crunch cost$2.50 each .
When you get to the shop you find that there are only 5 Silky Bars left.

Write the contraints as a system of inequalities.

Let $S$ = number of Silky Bars: . ${\color{blue}S \,\geq\,0}$
Let $M$ = number of Munchie Crunches: . ${\color{blue}M \,\geq\,0}$

$S$ Silky Bars at $2 each: $2S$ dollars (cost) $M$ Munchie Crunches at$2.50 each: $2.5M$ dollars (cost)
The total cost is: . $2S + 2.5S$, which is at most \$20.00.
. . We have: . ${\color{blue}2M + 2.5S \:\leq \:20}$

There are only 5 Silky Bars left: . ${\color{blue}S \:\leq\:5}$

There are the inequalties: . $\begin{Bmatrix}0\:\leq\:S \:\leq \:5 \\ \\[-3mm] M \:\geq\:0 \\ \\[-3mm] 2S + 2.5M \: \leq \: 20 \end{Bmatrix}$