Albert Durt, an Oklahoma State agriculture major, wants to determine the quantit
ID: 2936934 • Letter: A
Question
Albert Durt, an Oklahoma State agriculture major, wants to determine the quantities of various grains to feed the school’s cattle. The daily diet must contain at least 20 mg of protein, at least 70 mg of calcium, at least 4000 calories, and no more than 12 mg of iron. Albert is considering the use of corn, barley, oats and wheat.
Corn
Barley
Oats
Wheat
Protein mg/lb
10
9
11
8
Calcium mg/lb
50
45
58
50
Iron mg/lb
9
8
7
10
Calories per lb
1000
822
850
9000
Cost per lb
$.55
$.45
$.40
$.50
Write the LP formulation to help Albert determine the daily diet mix for the cattle to minimize cost
Corn
Barley
Oats
Wheat
Protein mg/lb
10
9
11
8
Calcium mg/lb
50
45
58
50
Iron mg/lb
9
8
7
10
Calories per lb
1000
822
850
9000
Cost per lb
$.55
$.45
$.40
$.50
Explanation / Answer
Let x1 be the number of units of Corn
x2 be the number of units of Barley
x3 be the number of Oats
x4 be the number of wheat
The objective function is
Min Z = 0.55x1 + 0.45x2 + 0.40x3 + 0.50x4
Subject to function
10x1 + 9x2 + 11x3 + 8x4 >=20 (Protein constraint)
50x1 + 45x2 + 58x3 + 50x4 >= 70 (Calcium Constraint)
9x1 + 8x2 + 7x3 + 10x4 <=12 ( Iron constrain)
1000x1 + 822x2 + 850x3 + 9000x4 >= 4000 ( Calories per)
Non negative constrain x1, x2, x3 and x4 >= 0
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