Show all steps$/$formaulas$/$constraints in Excel use solver must be linear model LOUISIANA FORGEWORKS $(25$ POINTS$)$

Louisiana Forgeworks manufactures custom steel and aluminum parts using several hot forges. $($Hot forging is a

manufacturing process involving the shaping of metal under high heat using compressive forces.$)$ Four of these

forges use natural gas $($NG$1,$ NG$2,$ NG$3,$ and NG$4)$ and two are coal$-$fired $($CF$1$ and CF$2).$ Louisiana Forgeworks has

received an order for $2800$ aluminum connecting rods. The table below summarizes the manufacturing costs

associated with producing these rods on each forge along with the available capacity on each forge. The fixed cost is a

setup cost associated with firing up each forge, and is incurred once if and only if any rods are produced on that

forge; the variable cost is incurred for each rod produced on the forge.

There are two additional restrictions. First, there is only enough natural gas remaining to produce $1800$ rods in total

across the four natural gas forges. Additional natural gas can be purchased, but this extra gas costs $$5$ for each rod

produced beyond the $1800$ across these four forges $($effectively adding $$5$ to the variable cost$).$ Second, because of

pollution concerns, at most one of the coal$-$fired forges $($ CF $1$ and CF $2)$ can be operated during the production period.

Which forges should be operated and how many connecting rods should be produced on each forge so as to

minimize the total cost of meeting this order? Set up a linear programming spreadsheet model $($with binary variables

if and only if necessary$),$ and solve it using Solver.