this is a linear programing problem A health food store packages a nut sampler c
ID: 3028277 • Letter: T
Question
this is a linear programing problem
A health food store packages a nut sampler consisting of walnuts, pecans, and almonds. Suppose each ounce of walnuts contains 12 units of protein and 3 units of iron and costs 12 cents, each ounce of pecans contains 1 unit of protein and 3 units of iron and costs 9 cents, and each ounce of almonds contains 2 units of protein and 1 unit of iron and costs 6 cents. If each package of the nut sampler is to contain at least 24 units of protein and at least 18 units of iron, how many ounces of each type of nut should be used to minimize the cost of the sampler?Explanation / Answer
Let , X1 unit of walnuts , x2 unit of pecans, x3 unit unit of almonds repectively...
MinZ=12x1+9x2+6x3
Subject to,
12x1+x2+2x324
3X1+3X2+X318
X1, x2, x30
The dual of the primal problem is
MaxZw=24w1+18w2
S.t
12w1+3w212
w1+3w29
2w1+w26
w1, w20
The dual can be rewritten as
MaxZw=24w1+18w2+0.w3+0.w4+0.w5
S.t
12w1+3w2+w3+0.w4+0.w5=12
w1+3w2+0.w3+w4+0.w5=9
2w1+w2+0.w3+0.w4+w5=6
w1, w2, w3, w4, w50
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