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# Tools for Business Decisions - Exercises 3

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• ### Tools for Business Decisions - Exercises 3

1. 1. 27C0100 Tools for Business Decisions kari.silvennoinen@hse.ﬁ
2. 2. Case 1 Merton Truck Company 2
3. 3. Exercise set 3 • Despite what’s on the ﬁrst page, returning by e-mail is not ok. Return your answers to the box. kari.silvennoinen@hse.ﬁ 3
4. 4. Merton Truck Company • Objective function: Unit contribution = selling price – variable costs = selling price – [direct material + direct labor + variable overhead]  • Model 101 contribution = \$3,000 • Model 102 contribution = \$5,000 • Objective function: kari.silvennoinen@hse.ﬁ 4
5. 5. MTC: Constraints M101 M102 Engine assembly 1 2 ≤ 4000 Metal stamping 2 2 ≤ 6000 Model 101 assembly 2 0 ≤ 2500 Model 102 assembly 0 3 ≤ 4500 1. (a) M101 = 2000, M102 = 1000, total contribution = \$11 000 000 (b) shadow price for assembly = \$2 000 (c) & (d) Allowable increase = 500 2. See (c) & (d), above 500 shadow price = 0, so maximum is 500 3. No Model 103 production. Lost contribution (from shadow prices) = 0,8*2000 + 1,5*500 + 1*0 + 0*0 = \$2350 < additional contribution \$2000 kari.silvennoinen@hse.ﬁ 5
6. 6. Merton Truck Company 4. No overtime production. Additional variables and constraints: M101OT M102OT Engine assembly OT 1 2 ≤ 2000 Metal stamping 2 2 ≤ 6000 Model 101 assembly 2 0 ≤ 2500 Model 102 assembly 0 3 ≤ 4500 Contributions (to objective function): M101OT = \$2400, M102OT = \$3800 Optimal product mix: M101 = 1500, M102 = 1250, M101OT = 0, M102OT = 250 New total proﬁt = 11,7 M\$ -kari.silvennoinen@hse.ﬁ 0,75 M\$ (additional ﬁxed cost) < 11 M\$ 6 (original solution)
7. 7. Merton Truck Company 5. No marketing constraint. Additional constraint: M101 M102 Sales mix 1 -3 ≥0 New optimal solution: M101 = 2250, M102 = 750, total proﬁt = 10,5 M\$ < 11 M\$ (original solution) (Also: in general, additional constraints kari.silvennoinen@hse.ﬁ 7
8. 8. Auto Assembly a) FT: 3800, CC: 2400, Proﬁt: 26,64 million b) No, current demand isn’t even met. c) FT: 3250, CC: 3500, Proﬁt 30,60 million d) 30,6 - 26,64 = 3,96 million e) FT: 3000, CC: 4000, Proﬁt 30,30 million kari.silvennoinen@hse.ﬁ 8
9. 9. Auto Assembly h) FT: 1500, CC: 3500, Proﬁt 24,30 million i) FT: 1875, CC: 3500, Proﬁt 25,65 > a) j) f) is the most optimal choice kari.silvennoinen@hse.ﬁ 9
10. 10. Ken and Larry, Inc. a) Chocolate: 0, Vanilla: 300, Banana: 75 b) Solution will change, proﬁts will increase c) Solution won’t change, proﬁts will decrease d) Solution will change, proﬁts decrease by \$3 e) Yes, the shadow price is higher than cost f) Final value: 180 (LHS constraint), Shadow price: 0 (Not binding), Constraint RHS: 200, Allowable increase: Inﬁnity (Not binding), Allowable decrease: 20 (LHS + 20 = RHS) kari.silvennoinen@hse.ﬁ 10