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1. Consider a portfolio manager with the following constraints: (1) if she purchases security j, she must purchase at least 200 shares; and (2) she may not purchase more than 1000 shares of security j. She can, however, buy zero shares. Let Xj be the number of shares of security j purchased. Using a binary constraint Y, write the constraint(s) to meet these purchasing rules. (2 pts)   2. A chemical company produces three products: (F)uel, (S)olvent and (D)etergent. Let F, S, and D represent the amount of each product they produce. They use three limited materials, with constraints: 0.4F + 0.5S + 0.6D ≤ 20 Material 1 0.2S + 0.1D ≤ 5 Material 2 0.6F + 0.3 S + 0.3 D ≤ 21 Material 3 F, S, D ≥0 They also have a setup cost to produce each product and a maximum available production for each product. Specifically: Product Profit Margin per unit Set up cost Maximum Production F $40 $200 50 S $30 $50 25 D $50 $400 40 Let YF, YS and YD be binary variables. Which objective function and constraints below will we need to add to the above material constraints to solve this problem as a profit maximization? (2 pts) A. Max 40F + 30S + 50D – 200F – 50 S – 400 D F ≤ 40 YF¬ S ≤ 30 YS¬ D ≤ 50 YD¬ B. Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD F = 50 YF¬ S = 25 YS¬ D = 40 YD¬ C. Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD F ≤ 50 YF¬ S ≤ 25 YS¬ D ≤ 40 YD¬ D. Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD F ≤ YF¬ S ≤ YS¬ D ≤ YD¬   3. Consider the transportation/assignment problem below. Assume Xij is the path between nodes i and j and the cost table represents cost per unit shipped along that path. a. Use the above information to calculate the total cost to ship: (3 pts) 200,000 along x14 400,000 along X25 75,000 along X15 75,000 along X35 225,000 along X36 b. Is it possible to satisfy all the demand in this problem? (1 pt) (circle one) Yes No Can Not Be Determined  4. Given the following three goal constraints: 5 X1 + 6 X2 + 7 X3 + d1- - d1+ = 89 3 X1 + X2 + 3 X3 + d2- - d2+ = 27 and a solution (X1, X2, X3) = (7, 2, 5), What values do the deviational variables assume? (4 pts) d1- = _____ d2- = _________ d1+ = ___________ d2+ = _________ 5. MonarchsMatter is planning its next informational campaign and has identified a variety of locations to which it can send speakers and informational material. These locations vary in the cost it would take to reach them and the expected number of people they would reach at each event. Due to constraints on staffing, and goals to allocate minimum donor dollars to this project so that more can go to research budgets, they have identified two alternative plans. Plan 1 sends volunteers to the highest turn-out events available for their staffing schedule. It will yield 370,540 in population reached but would cost $46,000 to implement. Plan 2 sends volunteers to the cheapest locations as available with their staffing schedule. It will yield only 152,134 in population reached, but would also only cost $30,500 to implement. They set a Minimax problem as shown below with objective value cell “M” (E5). Assume we get a calculated resulting budget of TestBudget and calculated resulting Exposure of TestExp in cells B2 and B3. Complete the minimax formulation below: A. Use the information and notation above to fill in the numbers or formulas for the white spaces of the table below. You can write your results using the names of cells (e.g. TestExp) or the cell reference (e.g. B3) (4 pts) C2: C3: D2: D3: B. Write the required minimax constraints using the above table (4 pts):

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1. Consider a portfolio manager with the following constraints: (1) if she purchases security j, she must purchase at least 200 shares; and (2) she may not purchase more than 1000 shares of security j. She can, however, buy zero shares.

Let Xj be the number of shares of security j purchased.

Using a binary constraint Y, write the constraint(s) to meet these purchasing rules. (2 pts)

Yj * Xj ≤ 1000
Yj * Xj ≥ 200
Yj = 1 if portfolio manager decide to by certain shares, or Yj = 0 if portfolio manager decide not to buy shares

2. A chemical company produces three products: (F)uel, (S)olvent and (D)etergent. Let F, S, and...

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