A feed company is developing a feed supplement from two grains A and B. Each kilogram of A contains 0.3 grams of protein and 0.2 grams of carbohydrates; each kilogram of B contains 0.9 grams of protein and 0.1 grams of carbohydrates. There must be at least 27 grams of protein and at least 8 grams of carbohydrates. Each kilogram of A costs 30 cents and each kilogram of B costs 50 cents.

a) prepare out the objective cost function.
b) prepare out the constraints this company faces.
c) List all corner points and determine which combination of items will produce the minimum cost.