A paint manufacturer produces two classes of products namely Premier-label and Standard-label, both of which are shipped in cylindrical barrels of a fixed size of 1000 litres each. In the factory are three pigment tanks, of equal capacities of 600 litres each, for holding and feeding red, green, and blue pigment separately to the primary mixer machine for producing the paints. These pigment tanks are filled before every cycle of production. And, during a cycle of production, no replenishment of pigments can be done. To produce one barrel of Premier-label paint, 5 litres of red pigment, 20 litres of green pigment, and 10 litres of blue pigment are demanded. To produce one barrel of Standard -label paint, 10 litres of red pigment, 6 litres of green pigment, and 8 litres of blue pigment are demanded. The paint manufacturer generates $30000 and $20000 per barrel of Premier-label and Standard-label paints respectively.

Determine the optimal average mix of Premier-label and Standard-label paints that the manufacturer should be produced in a cycle of production in order to maximize the profit.

Let x and y be the number of barrels of Standard-label and Premier-label paints that the manufacturer should produce in a cycle of production.

1. Set up a linear programming model and by using graphical method, determine the optimum solutions in terms of the number of barrels of Standard-label and Premier-label paints that the manufacturer should produce in a cycle of production in order to maximize profit per production cycle.
2. Determine the corresponding binding constraints.
3. Find the profit which is found to be maximum subject to the constraints.
4. Find the Shadow price of the capacity of the red pigment tank.
5. Find the Shadow price of the capacity of the green pigment tank.
6. While maintaining only the binding constraints determined in (b), determine the theoretical measuring-intervals of the capacity of the red pigment tank and the capacity of the green pigment tank.
7. Determine the allowable level of variations of the objective coefficients provided that the optimum solutions are not to be affected.

(All answers are to be either in integers or rounded to 2 decimal places.)

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