Hermione Granger is planning to make a special potion The po

Hermione Granger is planning to make a special potion. The potion needs Dragon Nails, Phoenix Feathers, and GoldenFish Skin in at least the amounts given in the following table.

Unfortunately, it is impossible for Hermione to obtain these three ingredients directly. However, three kinds of pre-mixed potion are available. Each of these three pre-mixed potions\' content, inventory and price per unit (1000 g) are given in the following table.

Due to a special chemical interaction of these potions\' solvents, Hermione also needs to make sure that the total amount of potion A that will be used to make the special potion would not exceed 20% of the special potion\'s total weight.

Hermione\'s question is:

How much of each pre-mixed potion should be used in her special potion such that she can satisfy the special potion\'s requirements at a minimum cost?

Hermione decides to solve this problem using linear programming. She formulates the decision variables as follows.

X = the amount of pre-mixed potion A (in 1000 g) to be used.

Y = the amount of pre-mixed potion B (in 1000 g) to be used.

Z = the amount of pre-mixed potion C (in 1000 g) to be used.

1. What is the objective function?

2. What is the constraint for the minimum amount of GoldenFish Skin required?

3. What is the constraint for the inventory availability of pre-mixed potion B?

4.What is the constraint for Potion A\'s 20% weight constraint in the special potion?

Solution

1. Objective function is

minimize 10A+8B+7C

2.

5X+15Y+5Z=18

3

5A+15B+5C=8Y

4.

0.20A=12D+14P+18G