Solutions to Assignment 1

• Problem 2-3
• Problem 2- 4
• Problem 2-5
• Problem 2-6
• Problem 2-8
• Problem 2-9
• Problem 2-10

• 2-3 Let X1 and X2 be the number of the two products produced
  
  Max 12 X1 + 4 X2
  St:
  X1 + 2 X2 <= 800
  X1 + 3 X2 <= 1600
  2 X1 + 3 X2 <= 2000
  X1, X2 >= 0
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• 2-4. Let Xa, Xb, Xc be the number of A,B,C and Xd be the number of unpainted C
  
  Max 25 Xa + 20 Xb + 50 Xc + 30 Xd
  st
  3 Xa + Xb + 4 Xc + 4 Xd <=150
  4 Xa + 2 Xb + 5 Xc + 5 Xd <= 200
  5 Xa + 5 Xb + 4 Xc <= 300
  Xa ,Xb, Xc, Xd >= 0
  
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• 2-5 Let X1 , X2 and X3 be number of shares of Gofer Crude, Can Oil and Sloth

Petroleum purchased

Max 7 x1 + 3 x2 + 3 x4 
st
60 x1 + 25 x2 + 20 x3 <= 100,000 
    x1                <=  1,000
           x2         <=  1,000 
                   x3 <=  1,500 

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Min .45/16 x1 + .38/16 x2 + .27/16 x3

st
.62x1 + .55x2 + .27x3>= 8
.05x1 + .10x2 + .20x3 >=1
.03x1 + .02x2 + .01x3 >= 1/2

x1,x2,x3>=0


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• 2-8 Let T and P amount of turmeric and paprika made.
  Also let h1, h2 and h3 unused ingredients sold separately
  
  Max 3.25 T + 2.75 P + .60 h1 + .70 h2 + .55 h3
  st
  4T + 3P + h1 = 8,000
  2T + 2P + h2 = 9,000
  T + 3P + h3 = 7,000
  T <= 1,700
  P <= 600

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2-9 Let X1, X2 and X3 represent the amounts of three fertilizers used (in thousand pounds )

        Min 10 X1 + 8 X2 + 7 X3

st 

25 X1 + 10 X2 + 5 X3 >= 10 

10 X1 + 5 X2 + 10 X3 >= 7 

 5 X1 + 10 X2 + 5 X3 >= 5 

 X1, X2, x3 >= 0

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 Let xij be the quantity of product shipped from warehouse 
i to retailer j (e.g., x32 would represent the amount shipped from warehouse 
2 to retailer 3)
        Min 5x11 + 7x12 + 6x13 + 8x21 + 9x22 + 10x23 + 4x31
                + 3x32 + 11x33
                st
                x11 + x12 + x13 <= 50 (capacity of whse 1)
                x21 + x22 + x23 <= 275 (Capacity of whse 2)
                x31 + x32 + x33 <= 175 (Capacity of whse 3)
                x11 + x21 + x31 >= 100
                x12 + x22 + x32 >= 250
                x13 + x23 + x33 >= 175
                xij >=0 (i= 1,2,3; j=1,2,3)

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