# Thread: minimization problem (linear programming)

1. ## minimization problem (linear programming)

a veterenarian mixes two types of animal food: Food 1 and Food 2. Each unit of Food 1 costs 200 and contains 40 grams of fat, 30 grams of protein and 1200 calories. Each unit of Food 2 costs 250 and contains 80 grams of fat, 60 grams of protein, and 1600 calories. Suppose the vet wants each unit of the final product to yield not more than 360 grams of fat, at least 240 grams of protein and at least 9600 calories, how many grams of each type of ingredient should the vet use to minimize his cost?

*ive defined the variables and constraints. but not so sure about it. the problem is i cant find the feasible region and the optimal mix when the lines are put in a graph.

** Let X1= Food 1; x2= Food 2

objective function= minimize Z= 200x1+250X2

constraints:
1. 40x1 + 80x2 less than or equal to 360
2. 30x1 + 60x2 greater than or equal to 240
3. 1200x1 + 1600x2 greater than or equal to 9600
4. non negativity constraints

2. Your constraints look good to me.

It looks like you should get a tiny triangular feasibility region up against the y-axis, between the two parallel lines.

3. thanx! i wish there's a graphical solution being shown to me coz i do not see a triangular area in my graph ill try to plot the points again

4. Originally Posted by julesalvanette
thanx! i wish there's a graphical solution being shown to me coz i do not see a triangular area in my graph ill try to plot the points again
I changed x_2 into y
and x_1 into x

I've attached the corresponding graph.

5. thanks much! i got the same graph though. didn't know that small area's the feasible region my other problem is that of the optimal mix of the ingredients. given that there are three of them. thanks