Hi!

I'm studying for a midterm coming up in a few days for my quantitative methods class.

Could anyone help me? I was sick for a few lectures and am not sure how to go about this.

These are two questions in particular that I am having issues with.

**1) **A farmer prepares feed for livestock by combining two grains: Grain I and Grain II. Each kilogram of Grain I costs $0.60 and contains 2 units of protein, 5 units of iron, and 5 units of carbohydrates. Each kilogram of Grain II costs $0.80 and contains 4 units of protein, 1 unit of iron, and 6 units of carbohydrates. Each animal must receive at least 20 units of protein, 16 units of iron, and 46 units of carbohydrates per day. Formulatea linear programming model to help the farmer determine the amount of Grain I and Grain II to purchase so as to meet the nutritional requirements of the animals at the least possible cost. **Do Not Solve. (<-- I'm not sure why it says 'do not solve' at the end of the question**

**2)** Use the Graphical Method to solve both of the two linear programming problems below, as follows:

(i) Shade-in the feasible region;

(ii) Label all cornerpoints and determine their coordinates; and

(iii) Write the optimal values of the objective function and the decision variables clearly.

**A)**Maximize Z= 2 *x*+ 4 *y*

Subject to: 2*x*+ *y*≤ 40

* x*+ *y*≤ 25

3x - 2y0

x 0, y 0

**B****) **Minimize C= 6*x *+ 2 *y*

Subject to: 2 *x*+ *y*≥ 40

2 *x *+ 5 *y *≥ 160

2*x *≤ 3y

*x *≥0, *y*≥ 0

**If anyone could help me or point into the right direction it would be greatly appreciated!!**