Suppose a dairy farmer in Murfreesboro is concerned with developing a minimum co

Question

Suppose a dairy farmer in Murfreesboro is concerned with developing a minimum cost per day feed-mix from two sources, alfalfa (X) and corn (Y), which meets (or exceeds) certain nutritional requirements. The two feed ingredients have varying quantities of calcium, protein, and calories. The information concerning the two feeds, and the requirements is summarized in the table below. (Show all work)

X Y Requirements

Calcium 1 1 10

Protein 3 1 15

Calories 1 6 15

Cost/Unit $1 $2

1) Write about the objective function and constraint relationships.

2) Find the optimal values of the two feed ingredients using the graphical solution method to a linear programming problem.

Explanation / Answer

1)minimize P=1x+2y
1x+1y>=10
3x+1y>=15
1x+6y>=15

2)

Vertex     Lines Through Vertex     Value of Objective
(2.5,7.5) 1x+1y = 10; 3x+1y = 15   17.5
(9,1)      1x+1y = 10; 1x+6y = 15   11 Minimum
(0,15)     3x+1y = 15; x = 0        30
(15,0)     1x+6y = 15; y = 0        15

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