HW1 Solution (F2011)

HW1 Solution (F2011) - Solution to Homework Assignment 1...

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Unformatted text preview: Solution to Homework Assignment 1 (MGMT 30600 Fall 2011) Question 1 (15%): Chapter 1 Question 8 Decision variables: X1: number of automobiles to buy X2: number of SUVs to buy X3: number of trucks to buy Max 2000X1 + 4500X2 + 3850X3 s.t. 35000X1 + 40000X2 + 60000X3 < 2000000 X1 > 2 X2 > 2 X3 > 2 X1 > 2/3*(X1 + X2 + X3) (or 1/3*X1 2/3*X2 2/3*X3 > 0) X1, X2, X3 > 0 (Nonnegativity is implied by the constraints 24, so it may not be needed.) Question 2: Chapter 3 Question 4 See solution on the next two pages. 1 Question 3 (20%): Chapter 3 Question 8: parts a and b only (please submit your Excel spreadsheet model with formulas, answer report, and sensitivity report) The optimal solution is to extract gold from 2 tons of ore from the Abracadabra Mine, 4 tons of ore from the Busted Flush Mine, and 0 tons from the Castle Mine. The optimal (objective function) value is a maximum of 16 oz. extracted gold. 4 5 Question 4 (20%): Chapter 3 Question 9: parts a and b only (please submit your Excel spreadsheet model with formulas, answer report, and sensitivity report) The optimal solution is to make 1,000 hats, make 0 scarves, buy 0 hats, and buy 2,000 scarves. The optimal (objective function) value is a minimum cost of $6,000. 6 7 Question 5 (20%): the graph is The optimal solution is ( x, y) (1,4) (b) The optimal (objective function) value is -8. (c) The binding constraints are x + 3y >= 13 and 4x - y >= 0. (a) 8 ...
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