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Ch4hwsolutions - 2 Nowledge College(minimize hours of study...

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2. Nowledge College (minimize hours of study) Definition of decision variables: number of business courses number of nonbusiness courses a. Objective function and constraints Minimize: Subject to: 1) money: $60 $24 $3, X X 1 2 000 2) business: 3) nonbusiness: 4) total courses: b. Graphic analysis. Feasible region is defined by points A, B, and C. We see visually from the dashed iso-cost line that corner point C minimizes costs. X 1 X 2 120 200 1 2 X X 1 1 23 X 2 1 20 X 1 2 1 1 65 X X 1 2 , 0 X X
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c. Optimal solution is at corner point C, which lies at the intersection of the money and total courses constraints. This appears to be in the neighborhood of coordinates (40, 25). To algebraically find the intersection of these two constraints, we multiply the total courses constraint by 24, and then subtract it from the money constraint. 60 X 1 + 24 X 2 = 3,000 (24 X 1 + 24 X 2 = 1,560) 36 X 1 = 1,440 X 1 = 40 business courses Substituting X 1 into the money constraint, we get 60 (40) + 24 X 2 = 3,000 24 X 2 = 600 X 2 = 25 nonbusiness courses
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