A dairy farmer concludes that his small herd of cows will need at least 4550 pounds of protein in their winter feed, at least 26,880 pounds of total digestible nutrients (TDN), and at least 43,200 international units (IUs) of vitamin A. Each pound of alfalfa hay provides .13 pound of protein, .48 pound of TDN, and 2.16 IUs of vitamin A. Each pound of ground ears of corn supplies .065 pound of protein, .96 pound of TDN, and no vitamin A. Alfalfa hay costs $8 per 100-pound sack. Ground ears of corn costs $13 per 100-pound sack.
(a) Fill in the following chart:

(b) Let x be the number of pounds of alfalfa hay and y be the number of pounds of ground ears of corn to be bought. Give the inequalities that x and y must satisfy.
(c) Graph the feasible set for the system of linear inequalities.
(d) Express the total cost of buying x pounds of alfalfa hay and y pounds of ground ears of corn.

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| Alfalfa | Corn | Requirements Protein TDN Vitamin A Cost/lb