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Writing given constraint in algebraic forms

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Please see attached document for complete details, some of the signs may not print here.

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

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Solution decribes the steps in converting descriptive statement into algebraic expressions.

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Please see the attached file for complete detais. Some of the signs may not print here.

Solution 1

x2 < 0.6 ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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