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

$\displaystyle S$ Silky Bars at $2 each:$\displaystyle 2S$dollars (cost)$\displaystyle M$Munchie Crunches at$2.50 each: $\displaystyle 2.5M$ dollars (cost)
The total cost is: .$\displaystyle 2S + 2.5S$, which is at most $20.00. . . We have: .$\displaystyle {\color{blue}2M + 2.5S \:\leq \:20}$There are only 5 Silky Bars left: .$\displaystyle {\color{blue}S \:\leq\:5}$There are the inequalties: .$\displaystyle \begin{Bmatrix}0\:\leq\:S \:\leq \:5 \\ \\[-3mm] M \:\geq\:0 \\ \\[-3mm] 2S + 2.5M \: \leq \: 20 \end{Bmatrix}\$