Problem $1.$ ABC Refining extracts minerals from ore mined at two different sites $($Site $1$ and Site $2).$

$$ Ore mined from Site $1$ costs $$95$ per ton, while ore from Site $2$ costs $$125$ per ton to mine.

$$ Each ton of ore from Site $1$ contains $17\%(\mathrm{.}17)$ copper, $21\%(\mathrm{.}21)$ zinc, and $14\%(\mathrm{.}14)$ magnesium.

$$ Each ton of ore from Site $2$ contains $29\%(\mathrm{.}29)$ copper, $24\%(\mathrm{.}24)$ zinc, and $11\%(\mathrm{.}11)$ magnesium.

ABC Refining needs enough ore to extract at least $9$ tons of copper, at least $6\mathrm{.}5$ tons of zinc, and at least $5\mathrm{.}5$ tons of magnesium to fulfill their contracts. They would like to do so in a way that minimizes their total cost. How much ore do they need to mine from each of the $2$ sites?

a$.$ What are your decision variables $($Xs$),$ list them? What do they stand for $($units$)?$

b$.$ Write down your objective function and constraints below, include brief descriptions$/$explanations on the right.

Delete or add rows as needed. Don$$t forget the nonnegativity constraint.

s$.$t$.($subject to$$ the following constraints$)$

c$.$ What is the solution $($use Excel Solver to solve the problem$)?$ What does each variable $($x$)$ and the objective function equal to$?$

d$.$ Managerial interpretation. What does your solution, above, mean in plain English? $($See the problem$/$question this problem seeks to answer.$)$