Exercises 35.5 Homework
1.
Use Matlab to solve the primal problem in Section 35.3 with the following data:
- Available amounts are \(L = 900\text{,}\) \(F = 600\text{,}\) \(P = 250\)
- Each unit of wheat requires \(F_1 = 0.7\) units of fertilizer and \(P_1 = 0.2\) units of pesticide
- Each unit of barley requires \(F_2 = 0.5\) units of fertilizer and \(P_2 = 0.3\) units of pesticide
- The sell prices are \(S_1 = 60\) for wheat and \(S_2 = 70\) for barley.
One way is to convert this LP problem to the form (35.1.1) (including the nonnegativity requirements in the system of linear inequalities) and apply linprog(c, A, b). Another is to follow the examples in Section 35.4 (or read help linprog) and directly impose the lower bound of \(0\) on the variables.
In a comment, answer the questions: how should the land be used? What will the total revenue be? Will there be any leftover land, fertilizer, or pesticide, and if so, how much?
2.
Use Matlab to solve the dual problem in Section 35.3 with the same data as in Exercise 35.5.1.
In a comment, answer the questions: What prices should the planning board set? What will the total cost be?