Write the LP formulation for this problem A daily diet must

. Write the LP formulation for this problem

A daily diet must be constructed determining the type and amount of foods to meet certain nutritional requirements at minimum cost. The foods that can be included are tuna fish, milk, spinach and whole-wheat bread; the nutrients we consider are vitamins A, C, and D, and iron. Nutritional and cost data are given in the table below.

Nutrient

Per Gallon of Milk

Per Pound of tuna fish

Per Loaf of bread

Per Pound of spinach

Recommended daily allowance

Vitamin A

6,400 IU

237 IU

0 IU

34,000 IU

5,000 IU

Vitamin C

40 mg

0 mg

0 mg

71 mg

75 mg

Vitamin D

540 IU

0 IU

0 IU

0 IU

400 IU

Iron

28 mg

7 mg

13 mg

8 mg

12 mg

Cost

$1.95

$1.80

$0.75

$0.80

Solution

Decision variables:
X1: Gallons of Milk
X2: Pounds of tuna fish
X3: Loafs of bread
X4: Pounds of spinach

LP formulation:

Objective function-
Minimise cost, C(X1,X2,X3,X4) = 1.95X1 + 1.80X2 + 0.75X3 + 0.80X4

Subject to constraints-
6400X1 + 237X2 + 0X3 + 3400X4 >= 5000
40X1 + 0X2 + 0X3 + 71X4 >= 75
540X1 + 0X2 + 0X3 + 0X4 >= 400
28X1 + 7X2 + 13X3 + 8X4 >= 12
X1,X2,X3,X4 >= 0