Question $4$: DO EITHER $($A$)$ OR $($B$)$ FROM THE TWO PROBLEMS BELOW

$($A$)$ Table below shows the hourly cost of four types of manufacturing processes. It also shows the number of hours required of each process to produce three different products. Using matrices only solve the following:

$1.$ Determine cost of each process to produce $1$ unit of product $1.$

$2.$ Determine the cost to make $1$ unit of each product and

$3.$ Compute the total cost if we would like to produce

$10$ units of product $1,5$ units of product $2$ and $7$ units of product $3$

$\backslash$begin$\{$tabular$\}\{|$r$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Process & $\backslash$multirow$\{2\}\{*\}\{\backslash$begin$\{$tabular$\}\{$c$\}$

Hourly $\backslash \backslash$

cost $\backslash ((\backslash$$$)\backslash )$

$\backslash$end$\{$tabular$\}\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{$ Hours required to produce one unit $\}\backslash \backslash$

$\backslash$cline $\{3-5\}$ & & Product $1$ & Product $2$ & Product $3\backslash \backslash$

$\backslash$hline Lathe & $10$ & $6$ & $5$ & $4\backslash \backslash$

$\backslash$hline Grinding & $12$ & $2$ & $3$ & $1\backslash \backslash$

$\backslash$hline Milling & $14$ & $3$ & $2$ & $5\backslash \backslash$

$\backslash$hline Welding & $9$ & $4$ & $0$ & $3\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$