$[$Please write it in hand and use the table method and iterations$]$

An automobile manufacturing company would like to get a special outer part finishing in its

premium brand cars. The research department advises to do the heat treatment with at least

$40$ units of material A and $50$ units of material B daily for a specified time period. It also

advises the company that to get material A and material B$,$ the company has to buy ore P

and ore Q that have both material A and material B in a proportion. One unit of ore P consists

$2$ units of material A and $3$ units of material B and one unit of ore Q consists of $4$ units of

material A and $2$ units of material B$.$ These ores are available in wholesale markets at a cost

of $3\mathrm{.}00$ USD and$2\mathrm{.}50$ USD per unit of P and Q respectively. Now the problem of the

company is to decide how much of P and Q are to be purchased from the market to minimise

the total cost while the company get the required amounts of materials A and B$.$ Solve this

linear programming problem using Big M method.