A firm is producing two goods, A and B $.$it has two factories that jointly produce the two goods

in the following quantities$($per hours$)$:

The firm receive an order for $300$ units of A and $500$ units of B$.$ The cost of operating the two

factories are $10000$ and $8000$ per hour.

a$.$ Formulate the linear programming problem of minimising the total cost of meeting this

order.

b$.$ Write its dual and solve it by graphical method.

c$)$ Are both the criterion same?