Exam 7: Analytic Geometry and Nonlinear Systems

A restaurant supply company must ship at least 120 cases of cheese to two midwest restaurants. Each restaurant can accommodate at most 120 cases of cheese. Restaurant A already has 30 cases of cheese on hand, while restaurant B already has 24 cases. It costs $\$ 14.40$ to ship a case of cheese to restaurant A and $\$ 12$ to ship a case of cheese to restaurant B. How many cases should be shipped to each restaurant to minimize cost? What is the minimum cost?

Solve the following system using one of the row echelon methods. 3 x+y-z =-2 -2 x+6 y+5 z =1 x+2 y+2 z =3

Solve the system by using Cramer's rule. 3 x+2 y =8 -5 x+4 y =-17

Suppose that $A$ is a $3 \times m$ matrix and $B$ is a $m \times 2$ matrix. (a) Can $A B$ be found? If so, give the dimensions of the resulting matrix. (b) Can $B A$ be found? If so, give the dimensions of the resulting matrix. (c) Does $A B=B A$ ? Explain why or why not. (d) If $C$ and $D$ are each square matrices, will $C D$ always exist?

The solution set of a system of inequalities is shown below. Which of the following systems is it? (a) $2 y-x \leq-4$ $y \geq-x^{2}-8 x-9$ (b) $2 y-x \geq-4$ $y \geq-x^{2}-8 x-9$ (c) $2 y-x \leq-4$ $y \leq-x^{2}-8 x-9$ (d) $2 y-x \geq-4$ $y \leq-x^{2}-8 x-9$

Find the partial fraction decomposition for the rational expression $\frac{5 x^{2}+2 x+1}{(x-1)(x+1)^{2}}$ .

Solve the system by using Cramer's rule. $3 x+12 y=5$ $9 x-8 y=4$

The solution set of a system of inequalities is shown below. Which of the following systems is it? (a) $2 y-3 x \geq 8$ $y \leq x^{2}+6 x+7$ (b) $2 y-3 x \leq 8$ $y \leq x^{2}+6 x+7$ (c) $2 y-3 x \geq 8$ $y \geq x^{2}+6 x+7$ (d) $2 y-3 x \leq 8$ $y \geq x^{2}+6 x+7$