Suppose that a linear program with bounded feasible region has I optimal extreme points v1, ·, vl. Prove that a point is optimal for the linear program if and only if it can be expressed as a convex combination of v1, vl.

23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.