Discuss the below:
1. Constraint
Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement SHOULD be written as:
a) x2 > 0.60
b) x2 > 0.60(x2 + x7 +x8)
c) 0.4x2 - 0.6x7 - 0.6x8 < 0
d) 0.4x2 - 0.6x7 - 0.6x8 > 0
e) -0.4x2 + 0.6x7 + 0.6x8 < 0
2. Blend Constraint
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 supply constraint for component 1.
a) x21 + x22 8000
b) x12 + x22 8000
c) x11 + x12 8000
d) x21 + x22 8000
e) x11 + x12 8000
3. Blend Constraint
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) < 0
b) x11 + .35 (x11 + x21) < 0
c) x11 + .35 (x11 + x12) < 0
d) .65x11 - .35x21 0
4. Marketing Problem Constraint
If Xab = the production of product a in period b, then to indicate that the limit on production of the company's "3" products in period 2 is 400,
a) X32 400
b) X21 + X22 + X23 400
c) X12 + X22 + X32 400
d) X12 + X22 + X32 400
e) X23 400