Chapter 5.3, Problem 3MP

A chicken farmer can buy a special food mix $A$ at $20\cancel{\text{c}}$ per pound and a special food mix $B$ at $40\cancel{\text{c}}$ per pound. Each pound of mix $A$ contains $3,000$ units of nutrient $N_1$ and $1,000$ units of nutrient $N_2$ ; each pound of mix $B$ contains $4,000$ units of nutrient $N_1$ and $4,000$ units of nutrient $N_2$. If the minimum daily requirements for the chickens collectively are $36,000$ units of nutrient $N_1$ and $20,000$ units of nutrient $N_2$, how many pounds of each food mix should be used each day to minimize daily food costs while meeting (or exceeding) the minimum daily nutrient requirements? What is the minimum daily cost? Construct a mathematical model and solve using the geometric method.