Achicken farm orders bags of feed from two farmers. store x charges $20 per bag, and store y charges $15 per bag. the farm must obtain at least 60 bags per week to care for the chickens properly. store y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store x as from store y. the chicken farm wants to minimize the cost of ordering feed. let x represent the number of bags of feed from store x and y represent the number of bags of feed from store y. what are the constraints for the problem? mc021-1.jpg mc021-2.jpg mc021-3.jpg mc021-4.jpg mc021-5.jpg mc021-6.jpg mc021-7.jpg

The probrem is a linear programing probrem.
Linear programing is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.

In linear programming, we seek to maximize or minimize an objective function subject to some given conditions. Those conditions are refered to as the constraints.

For the given question, Here, the objective function is the cost of feeding the chikens per week.
Given that x represents the number of bags of feed from store X and y represents the number of bags of feed from store Y. And store X charges $20 per bag, and store Y charges $15 per bag.

Thus, we can represent the objective function as


We are given conditions as follows:

1.) The farm must obtain at least 60 bags per week to care for the chickens properly. This condition means that the sum of the number of bags of feed from store X and store Y must be greater than or equal to 60.
Mathematically, we have


2.) Store Y can provide a maximum of 40 bags per week. This means that the number of bags of feed bought from store X must be less than or equal to 40.
Mathematically, we have:


3.) The farm has committed to buy at least as many bags from store X as from store Y. This means that the number of bags of feed bought from store X must be greater than or equal to the number of bags of feed bought from store Y.
Mathematically, we have:


4.) For every linear programming problem, there is a general constraints which says that the values of the constraints must not be negative.
i.e. x and y must be greater than or equal to 0.
Mathematically, we have:


Therefore, the constraints to the linear programming problem given above are: