Find the graphical solution of each inequality. $$ 5 x-3 y \geq 15 $$

Find the graphical solution of each inequality. $$ y \geq-1 $$

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded. $$ \begin{array}{l} 2 x-y \geq 4 \\ 4 x-2 y<-2 \end{array} $$

MANUFACTURING-SHIPPING CosTS Steinwelt Piano manufactures uprights and consoles in two plants, plant I and plant II. The output of plant \(I\) is at most \(300 /\) month, whereas the output of plant II is at most \(250 /\) month. These pianos are shipped to three warehouses that serve as distribution centers for the company. To fill current and projected future orders, warehouse A requires a minimum of 200 pianos/month, warehouse B requires at least 150 pianos/month, and warehouse \(\mathrm{C}\) requires at least 200 pianos/month. The shipping cost of each piano from plant I to warehouse A, warehouse \(\mathrm{B}\), and warehouse \(\mathrm{C}\) is \(\$ 60, \$ 60\), and $\$ 80$, respectively, and the shipping cost of each piano from plant II to warehouse A, warehouse \(\mathrm{B}\), and warehouse \(\mathrm{C}\) is $\$ 80, \$ 70\(, and \)\$ 50$, respectively. What shipping schedule will enable Steinwelt to meet the warehouses' requirements while keeping shipping costs to a minimum?

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded. $$ \begin{aligned} x-3 y & \geq-18 \\ 3 x-2 y & \geq 2 \\ x-3 y & \leq-4 \\ 3 x-2 y & \leq 16 \\ x \geq 0, y & \geq 0 \end{aligned} $$

Bata Aerobics manufactures two models of steppers used for aerobic exercises. Manufacturing each luxury model requires \(10 \mathrm{lb}\) of plastic and 10 min of labor. Manufacturing each standard model requires \(16 \mathrm{lb}\) of plastic and \(8 \mathrm{~min}\) of labor. The profit for each luxury model is \(\$ 40\), and the profit for each standard model is \(\$ 30\). If $6000 \mathrm{lb}$ of plastic and 60 laborhours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day in order to maximize its profit? What is the optimal profit?