sol7 - we would be willing to pay 1 + 0 . 75 = 1 . 75)....

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 7: Solution notes 1). (a). Graphically, fnd the range o± values o± b 2 ±or which the current basis remains optimal. The optimal solution is when both constraints are binding. As b 2 increases, the optimal solution goes towards point (4,0), where b 2 = 16. Similarly, when b 2 decreases the intersection point moves towards (0,8) where b 2 = 8, so 8 b 2 16. (b). Calculate the shadow price o± the second constraint. Solve 2 x 1 + x 2 = 8 and 4 x 1 + x 2 = 10+Δ, get x 1 = 1 + Δ / 2, x 2 = 6 - Δ, z = 9 + Δ / 2 so shadow price is 1 / 2. (c). Graphically fnd the range o± c 1 ±or which the current basis remains optimal. 2 c 1 4. 2). (a). What is the most the company should pay ±or an additional unit o± raw material? Dual price o± the second constraint (row 3) which is 0.50. (b). What is the most the company should pay ±or an additional hour o± labor? Dual price o± the frst constraint (row 2) which is 1.75. (Or can look at the third constraint, and i± we are allowed to buy 1 more hour o± labor, at the regular price o± 1, we would increase our proft by 0.75, and so
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Unformatted text preview: we would be willing to pay 1 + 0 . 75 = 1 . 75). (c). What would product 1 have to sell or to make it desirable or the company to produce it? Its current sale pice plus the reduced cost 6.25. (d). I 100 hours o labor could be purchased, what would the companys proft be? The increase is 100-90 = 10 18 which is the allowable increase. The new proft would be 97 . 5 + 10 . 75 = 105. (e). Find the new optimal solution o product 3 sold or $15. The increase is 15-13 = 2 3 which is the allowable increase. The new proft would be 97 . 5 + 2 7 . 5 = 112 . 5. (e). A 4th product is being considered. It sells or $10 and requires 4 hours o labor and 3 units o raw material. Shoul the company produce any o this new product in a new optimal solution? Price out the new product: 4 1 . 75 + 3 . 5 = 8 . 5 < 10 so yes, the company would want to make this 4th product....
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