A dietician wishes to mix two types of food in such a way that the vitamin contends of the mixture contains at least 8 units of vitamin A and 10 units of vitamin B. Food I contains 2 units per Kg of vitamin A and 1 unit per Kg of vitamin B while food II contains 1 unit per Kg of vitamin A and 2 units of vitamin B. It costs 5 birr per Kg to purchase food I and birr 8 per Kg to purchase food II. Prepare the linear programming model for the problem.
Let x be the number of kilograms of food I to be purchased.
Let y be the number of kilograms of food II to be purchased.
The objective is to minimize the cost, which is 5x + 8y.
Subject to the constraints:
- The vitamin A content in the mixture should be at least 8 units: 2x + y ≥ 8
- The vitamin B content in the mixture should be at least 10 units: x + 2y ≥ 10
- The number of kilograms of both food I and food II must be non-negative: x ≥ 0, y ≥ 0
Therefore, the linear programming model for the problem is:
Minimize: 5x + 8y
Subject to:
2x + y ≥ 8
x + 2y ≥ 10
x ≥ 0
y ≥ 0