$15$ Reddy Mikks produces both interior and exterior paints from two raw materials, M$1$

and M$2.$

The following table provides the basic data of the problem:

Tons of raw material per ton of

Exterior paint Interior paint Maximum daily

availability

$($tons$)$

Raw material,

M$1$

$6424$

Raw material,

M$2$

$126$

Profit per ton

$($$$1000)$

$54$

The daily demand for interior paint cannot exceed that for exterior paint by more than $1$ ton.

Also, the maximum daily demand for interior paint is $2$ tons.

a$)$ Determine the optimum $($best$)$ product mix of interior and exterior paints that

maximizes the total daily profit.

b$)$ Write the dual of the above problem and find its solution.

c$)$ What does the dual solution, dual objective and dual constraints signify.