1. Which of the following constraints, applied collectively, does not contribute

Question

1. Which of the following constraints, applied collectively, does not contribute to defining the feasible region? a) X1 + X2 <= 10 b) X1 – X2 <=10 c) X1 + 3X2 <= 20 d) X1, X2 >= 0
2. The feasible region does not include: a) interior points. b) boundary points. c) points at which at least one of the decision variables is zero. d) points which violate at least one of the functional or non-negativity constraints.
3. Squire Leathers produces two sizes of wallets from cowhide. The first requires 60 square inches of cowhide and the second requires 100 square inches. The company has 1000 square feet of cowhide. Part of the model is: a) 60X1 + 100X2 >=144,000 b) 60X1 + 100X2 <=144,000 c) 60X1 + 100X2 = 144,000 d) 60X1 <=144,000 and 100X2 <=144,000
4. Hong Securities has $300,000 to invest in four stocks and three bonds. X1, X2, X3, and X4 denote the amounts invested in each of the stocks, and Y1, Y2, and Y3 equal the amounts invested in each of the three bonds. Which of the following shows that at least 40% of the investment in stocks must be in stock 1? a) X1 >=120,000 b) X1 - .4X2 -.4X3 - .4X4 >=0 c) .6X1 - .4X2 - .4X3 - .4X4 >= 0 d) X1 >= .4(X2 + X3 + X4 + Y1 + Y2 + Y3)
5. The functional constraints of a linear model with nonnegative variables are 3X1 + 5X2 <=16 and 4X1 + X2 <=10. Which of the following points could not be an optimal solution for the model? a) X1 = 2.5, X2 = 0 b) X1 = 0, X2 = 3.2 c) X1 = 1, X2 = 2.25 d) X1 = 2, X2 = 2
6. In a standard transportation model, each objective function coefficient represents the: a) total cost of shipping from a source to a destination node. b) fixed cost of utilizing the route between a source and destination node. c) unit cost of shipping from a source to a destination node. d) negative “unit cost” of not using the route between a source and a destination node.
7. Which of the following cannot model a blocked route on a transportation model? a) A very large objective coefficient. b) A constraint on shipment equal to zero. c) Excluding the cell from the list of changing cells in the Excel Solver parameters. d) Assigning an objective function coefficient of zero. 1. Which of the following constraints, applied collectively, does not contribute to defining the feasible region? a) X1 + X2 <= 10 b) X1 – X2 <=10 c) X1 + 3X2 <= 20 d) X1, X2 >= 0
2. The feasible region does not include: a) interior points. b) boundary points. c) points at which at least one of the decision variables is zero. d) points which violate at least one of the functional or non-negativity constraints.
3. Squire Leathers produces two sizes of wallets from cowhide. The first requires 60 square inches of cowhide and the second requires 100 square inches. The company has 1000 square feet of cowhide. Part of the model is: a) 60X1 + 100X2 >=144,000 b) 60X1 + 100X2 <=144,000 c) 60X1 + 100X2 = 144,000 d) 60X1 <=144,000 and 100X2 <=144,000
4. Hong Securities has $300,000 to invest in four stocks and three bonds. X1, X2, X3, and X4 denote the amounts invested in each of the stocks, and Y1, Y2, and Y3 equal the amounts invested in each of the three bonds. Which of the following shows that at least 40% of the investment in stocks must be in stock 1? a) X1 >=120,000 b) X1 - .4X2 -.4X3 - .4X4 >=0 c) .6X1 - .4X2 - .4X3 - .4X4 >= 0 d) X1 >= .4(X2 + X3 + X4 + Y1 + Y2 + Y3)
5. The functional constraints of a linear model with nonnegative variables are 3X1 + 5X2 <=16 and 4X1 + X2 <=10. Which of the following points could not be an optimal solution for the model? a) X1 = 2.5, X2 = 0 b) X1 = 0, X2 = 3.2 c) X1 = 1, X2 = 2.25 d) X1 = 2, X2 = 2
6. In a standard transportation model, each objective function coefficient represents the: a) total cost of shipping from a source to a destination node. b) fixed cost of utilizing the route between a source and destination node. c) unit cost of shipping from a source to a destination node. d) negative “unit cost” of not using the route between a source and a destination node.
7. Which of the following cannot model a blocked route on a transportation model? a) A very large objective coefficient. b) A constraint on shipment equal to zero. c) Excluding the cell from the list of changing cells in the Excel Solver parameters. d) Assigning an objective function coefficient of zero. 1. Which of the following constraints, applied collectively, does not contribute to defining the feasible region? a) X1 + X2 <= 10 b) X1 – X2 <=10 c) X1 + 3X2 <= 20 d) X1, X2 >= 0
2. The feasible region does not include: a) interior points. b) boundary points. c) points at which at least one of the decision variables is zero. d) points which violate at least one of the functional or non-negativity constraints.
3. Squire Leathers produces two sizes of wallets from cowhide. The first requires 60 square inches of cowhide and the second requires 100 square inches. The company has 1000 square feet of cowhide. Part of the model is: a) 60X1 + 100X2 >=144,000 b) 60X1 + 100X2 <=144,000 c) 60X1 + 100X2 = 144,000 d) 60X1 <=144,000 and 100X2 <=144,000
4. Hong Securities has $300,000 to invest in four stocks and three bonds. X1, X2, X3, and X4 denote the amounts invested in each of the stocks, and Y1, Y2, and Y3 equal the amounts invested in each of the three bonds. Which of the following shows that at least 40% of the investment in stocks must be in stock 1? a) X1 >=120,000 b) X1 - .4X2 -.4X3 - .4X4 >=0 c) .6X1 - .4X2 - .4X3 - .4X4 >= 0 d) X1 >= .4(X2 + X3 + X4 + Y1 + Y2 + Y3)
5. The functional constraints of a linear model with nonnegative variables are 3X1 + 5X2 <=16 and 4X1 + X2 <=10. Which of the following points could not be an optimal solution for the model? a) X1 = 2.5, X2 = 0 b) X1 = 0, X2 = 3.2 c) X1 = 1, X2 = 2.25 d) X1 = 2, X2 = 2
6. In a standard transportation model, each objective function coefficient represents the: a) total cost of shipping from a source to a destination node. b) fixed cost of utilizing the route between a source and destination node. c) unit cost of shipping from a source to a destination node. d) negative “unit cost” of not using the route between a source and a destination node.
7. Which of the following cannot model a blocked route on a transportation model? a) A very large objective coefficient. b) A constraint on shipment equal to zero. c) Excluding the cell from the list of changing cells in the Excel Solver parameters. d) Assigning an objective function coefficient of zero.

Explanation / Answer

1) A feasible region is a region of the data where all possible combinations satisfy

We see that adding (b) and (c) will give the same equation as that of (a)

Hence a combination of (b)+(c) and (a) do not satisfy the feasiblity region

2)

A feasible region is a region of the data where all possible combinations satisfy

hence it cannot have any points which violates one or many contrainstraints

Hence(d)

3)

Given

model 1 needs 60

model 2 needs 100

Total =1000

Hence

60X1+100X2=<1000

So if it is a part of the model

we have 60X1+100X2=<1000*144

So option (b)

4)

We need alteast 40% in stock 1

40% of 300,000 =120,000

X1>-=120,000

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