# Economics

Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2
What is the sensitivity range for the third constraint, y ≥ 2?
0 to 4
2 to 5.33
0 to 5.33
4 to 6.33
Question 16
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to \$50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?
X1 ≤ 0.35

X1 = 0.35 (50000)

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X1 ≤ 0.35(X1 + X2 +.X3)

X1 = 0.35(X1 + X2 +.X3)

Question 17
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to \$50,000 to invest.
An appropriate part of the model would be
15X1 + 47.25X2 +110 X3 ≤ 50,000
MAX Z =15X1 + 47.25X2 + 110X3
X1 + X2 +X3 ≤ 50,000
MAX Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)X3
Question 18
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

x1 + x2 + x5 ≤ 1

x1 + x2 + x5 ≥1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

x1 – x5 ≤ 1, x2 – x5 ≤ 1

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