Answer to Question #267730 in Operations Research for ezbee

Question

Directions: Establish the table of information and formulate the LP Model of the following:

1.) Rina needs at least 48 units of protein, 60 units of carbohydrates, and 50 units of fat each month. From each kilogram of food A, she receives 2 units of protein, 4 units of carbohydrates, and 5 units of fats. Food b contains 3 units of protein, 3 units of carbohydrates, and 2 units of fats. If food A costs Php110 per kilogram and food B costs Php 90 per kilogram. How many kilograms of each food should Sofia buy each month to keep costs at a minimum?

Answer 1

for x kg of A and y kg of B, you want to minimize

p = 100x₁ + 90x₂

subject to the conditions that

$2x_1+3x_2 \ge 46$

$4x_1+3x_2 \ge 60$

$5x_1+2x_2 \ge 50$

the optimal solution to the given LP problem is : x₁=7,x₂=10.67 and min z=1660.