91Ó°ÊÓ

Solve the given linear programming problems. An oil refinery refines types \(A\) and \(B\) of crude oil and can refine as much as 4000 barrels each week. Type A crude has 2 kg of impurities per barrel, type \(\mathrm{B}\) has \(3 \mathrm{kg}\) of impurities per barrel, and the refinery can handle no more than \(9000 \mathrm{kg}\) of these impurities each week. How much of each type should be refined in order to maximize profits, if the profit is \(\$ 4 /\) barrel for type \(\mathrm{A}\) and \$5/barrel for type B?

Solve the given inequalities. Graph each solution. $$\frac{1}{3}-\frac{L}{2}

Solve the given inequalities. Graph each solution. $$4<6 R+2 \leq 16$$

Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities. $$\begin{aligned} &2 y>x\\\ &y>1-x \end{aligned}$$

Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities. $$\begin{aligned} &y>x^{2}\\\ &y

give verbal statements equivalent to the given inequalities involving the number \(x\). x < -10 \text { or } 10 \leq x < 20

give verbal statements equivalent to the given inequalities involving the number \(x\). -1 \leq x < 3 \text { or } 5 < x < 7

graph the given inequalities on the number line. $$x \geq-1$$

graph the given inequalities on the number line. $$x \geq-3 \text { and } x < 5$$

Solve the given problems by setting up and solving appropriate inequalities. Graph each solution. Determine the values of \(x\) that are in the domain of the function \(f(x)=1 / \sqrt{3-0.5 x}\).