Ch03rp

# Ch03rp - 1 CHAPTER 3 MP REVIEW PROBLEMS 1. Let x1 = barrels...

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CHAPTER 3 MP REVIEW PROBLEMS 1. Let x 1 = barrels of beer produced x 2 = barrels of ale produced Then we should solve max z = 5x 1 + 2x 2 s.t. 5x 1 + 2x 2 60 2x 1 + x 2 25 x 1 , x 2 0 Graphically we find the optimal solution to be z = 60, x 1 = 10, x 2 = 5, x 1 = 12, x 2 = 0 is an alternative optimal solution. 2. Let x 1 = number of chocolate cakes baked x 2 = number of vanilla cakes baked Then we should solve max z = x 1 + .50x 2 s.t. 20x 1 + 40x 2 480 4x 1 + x 2 30 x 1 , x 2 0 Graphically, the optimal solution is found to be x 1 = 36/7, x 2 = 66/7, z = 69/7. 3. Let A = dollars invested in investment A B = dollars invested in investment B C = dollars invested in investment C Mt = dollars invested in money market funds at end of year t. Then the appropriate LP is Max z = 1.06M2 + 1.5C + 1.3A s.t. 100 = A + B +M0 .20B + 1.06M0 + .10A = C + M1 1.1B + 1.06M1 = M2 A 50, B 50, C 50 All variables 0 4. Let OIL = thousands of barrels of purchased oil HOS = thousands of barrels of non-cracked heating oil sold HOP = thousands of barrels of heating oil processed further AFS = thousands of barrels of non-cracked aviation fuel sold AFP = thousands of barrels of aviation fuel processed further 1

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Then we should solve max z = 40HOS + 90HOP - 40(OIL) + 130AFP + 60AFS st OIL 20 .5(OIL) = AFS + AFP .5(OIL) = HOS + HOP AFP + .75HOP 8 All variables 0 5. Let A = dollars invested in investment A B = dollars invested in investment B C = dollars invested in investment C Tt = dollars invested in T-Bills at the end of year t Then we should solve max z = 1.2C + 1.1T2 s.t. A + T0 = 100 1A + 1.1T0 = T1 + B 1.3A + 1.6B + 1.1T1 = C + T2 A, B, C 50 All variables 0 6. Let x 1 = Number of pounds of Alloy 1 used to produce one ton of steel and x 2 = Number of pounds of Alloy 2 used to produce one ton of steel. min z = 190x 1 /2000 + 200x 2 /2000 .03x 1 + .04x 2 70 Carbon Constraints .03x 1 + .04x 2 64 .02x 1 + .025x 2 36 Silicon Constraints .02x 1 + .025x 2 50 .01x 1 + .015x 2 18 Nickel Constraints .01x 1 + .015x 2 24 (42,000x 1 + 50,000x 2 )/2,000 45,000 (Tensile Const.) x 1 + x 2 = 2,000 x 1 0, x 2 0. 7. Let x ij = Number of tons of Steel j produced each month at Mill i. Then a correct formulation is min z = 10x 11 + 12x 21 + 14x 31 + 11x 12 + 9x 22 + 10x 32 s.t. 20x 11 + 22x 12 200(60) (Mill 1 Const.) 24x 21 + 18x 22 200(60) (Mill2 Const.) 28x 31 + 30x 32 200(60) (Mill 3 Const.) x 11 + x 21 + x 31 500(Steel 1 Demand) x 12 + x 22 + x 32 600 (Steel 3 Demand) 2
All variables 0 8. Let x 1 = Acres of Farm 1 devoted to corn. x 2 = Acres of Farm 1 devoted to wheat. x 3 = Acres of Farm 2 devoted to corn. x

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## Ch03rp - 1 CHAPTER 3 MP REVIEW PROBLEMS 1. Let x1 = barrels...

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