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Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1.
a. x11 + x12 (.35)(x11 + x21)
b. x11 .35 (x11 + x21)
c. x11 .35 (x11 + x12)
d. -.65x11 + .35x21 0
e. .65x11 - .35x21 0

In a multi-period scheduling problem the production constraint usually takes the form of :
a. beginning inventory + demand - production = ending inventory
b. beginning inventory - demand + production = ending inventory
c. beginning inventory - ending inventory + demand = production
d. beginning inventory - production - ending inventory = demand
e. beginning inventory + demand + production = ending inventory

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Machine Fixed cost to set up production runVariable cost per hose Capacity

1 750 1.25 6000
2 500 1.50 7500
3 1000 1.00 4000
4 300 2.00 5000

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.
a. y1 + y4 0
b. y1 + y4 = 0
c. y1 + y4 1
d. y1 + y4 0
e. y1 + y4 1

Max Z = 5x1 + 6x2
Subject to:17x1 + 8x2 136
3x1 + 4x2 36
x1, x2 0 and integer
What is the optimal solution?
a. x1= 6, x2 = 4, Z = 54
b. x1= 3, x2 = 6, Z = 51
c. x1= 2, x2 = 6, Z = 46
d. x1= 4, x2 = 6, Z = 56
e. x1= 0, x2 = 9 Z = 54

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