M&D produces two types of oil additives: O$1$ and O$2.$ Each additive cost $$1$ per liter to produce. M&D$$s management decided that at least $30$ liters of O$1$ and at least $20$ liters of O$2$ must be produced in the next week. There are $80$ kgs of raw material for production of additives. All this amount of raw material must be used. O$1$ requires $1$kg of raw material per $1$ liter. O$2$ requires $2$kgs of raw material per $1$liter. Help M&D management to find the minimum$-$cost solution.

M&D Solution

$1.$ Linear Programming Model

$2.$ optimal solution and objective funtion.

$3.$ extreme points and coordinates.

$4.$ constraint, binding$/$notbinding$.$ slack or surplus? and inertrepretation.

$5.$ a Graph.

$6.$What happens if in addition to the previous requirements, the cost of production of O$1$ will increase to $$2?($sensitivity$)$