Use Inequalities to Describe Limitations in a Situation
-A Steel $\$ 0.75$

Use Inequalities to Describe Limitations in a Situation
-A steel company produces two types of machine dies, part A and part B and is bound by the following constraints:
- Part A requires 1 hour of casting time and 10 hours of firing time.
- Part B requires 4 hours of casting time and 3 hours of firing time.
- The maximum number of hours per week available for casting and firing are 100 and 70 , respectively.
- The cost to the company is $\$ 0.75$ per part $A$ and $\$ 3.00$ per part $B$ . Total weekly costs cannot exceed $\$ 45.00$ .
Let $\mathrm { x } =$ the number of part A produced in a week and $\mathrm { y } =$ the number of part B produced in a week. Write a system of three inequalities that describes these constraints.

A)
$\begin{array}{r}x+4 y \leq 100 \\10 x+3 y \leq 70 \\0.75 x+3 y \leq 45\end{array}$

B) $\begin{array}{r}x+10 y \leq 100 \\4 x+3 y \leq 70 \\0.75 x+3 y \leq 45\end{array}$

C) $\begin{array}{r}x+10 y \geq 100 \\4 x+3 y \geq 70 \\0.75 x+3 y \leq 45\end{array}$

D)
$$\begin{array} { r r } x + & 4 y \leq 100 \\10 x + 3 y \leq & 70 \\3 x + 0.75 y \leq & 45\end{array}$$