Solving System of Inequalities with Examples

Graph the solution set for the of linear inequalities
${\displaystyle y<\frac{1}{3}x+1}$
${\displaystyle y\ge \frac{1}{3}x-2}$

You decide to make and sell two different gift baskets at your local outdoor market. Basket A contains 3 cookies, 6 chocolates, and 2 jars of jam and makes a profit of $12. Basket B contains 6 cookies, 3 chocolates, and 2 jars of jam and makes a profit of $15. You have just made 48 cookies, 36 chocolates, and 18 jars of jam. How many of each type of gift basket should you make to maximize the profit? a) State what you assign to x and y. Write the objective function. b) Write the three constraint inequalities. c) Find the axes intercepts of each of the above inequalities.

Graph the system of linar inequlities ${\displaystyle \{\begin{array}{c}2x-4y\le 0\\ 4x+2y\le 8\end{array}}$

Draw the graph of inequalities
${\displaystyle \{\begin{array}{c}|x-2|\le 5\\ |y-4|>2\end{array}}$

Graph the solution set of the system of inequalities.
${\displaystyle x-y\le 2x-y\le 2}$
${\displaystyle x\ge 3}$

Graph the solution set of the system of inequalities or indicate that the system has no solution.
${\displaystyle \{\begin{array}{c}x+y>4\\ x+y<-1\end{array}}$

Graph the Inequalities, and shade the feasible region
${\displaystyle 4x+5y\ge 12}$
${\displaystyle -x+2y\ge 2}$