A dairy farmer concludes that his small herd of cows will need at least 3, 850 p

Question

A dairy farmer concludes that his small herd of cows will need at least 3, 850 pounds of protein in their winter feed, at least 21, 120 pounds of total digestible nutrients (TDN), and at least 43, 600 international units (IUs) of vitamin A. Each pound of alfalfa hay provides 0.11 pound of protein, 0.44 pound of TDN, and 2.18 IUs of vitamin A. Each pound of ground ears of corn supplies 0.055 pound of protein, 0.88 pound of TDN, and no vitamin A. Alfalfa hay costs $1 per 100-pound sack. Ground ears of corn costs $1.60 per 100-pound sack. (a) Fill in the following chart. (Type an integer or a decimal.) (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. { greaterthanorequalto 3, 850 greaterthanorequalto 21, 120 greaterthanorequalto 43, 600, y greaterthanorequalto 0 (c) Graph the feasible set for the system of linear inequalities. The feasible set is left unshaded. Click the magnifying glass to enlarge the graph. (d) Express the cost of buying x pounds of alfalfa hay and y pounds of ground ears of corn. Cost is

Explanation / Answer

based on the information the table can be completed as follows

0.11x + 0.055y >= 3850

0.44x + 0.88 y >= 21, 120

2.18x + 0y >= 43, 600

objective function is

C = 1x + 1.60 y

x is number of pounds of alfalfa hay and y is number of pounds of ground ears of corn

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