Number of Regular shirts R

Transcription

1 Table 1.1 rossing points for ctivity 1.5 onstraint R D otton 1 12 Labour otton feasible region p Labour Figure 1.1 Graphical solution for the Just Shirts problem q otton Figure 1.2 The isoprofit method p Isoprofit Isoprofit line for a profit of 36 Labour Table 1.2 Profit at each corner point of the feasible region R D Profit Point 8 6 Point Point 12 6

2 1 otton Figure 1.3 Effect on the optimum solution when the profit changes Isoprofit Labour Table 1.3 rossing points for ctivity 1.1 onstraint R T udience 2 2 Total slots 5 5 Min. slots for radio 1 Min. slots for TV 1 5 Radio ads Number of TV ads T Total number of ads Feasible region udience TV ads Figure 1. Graphical solution for Example Number of radio ads R Table 1. Solution to ctivity 1.1 R T ost

3 Right hand side of constraints Figure 1.5 Setting up the formulae for Solver Number of shirts to make Total profit dd constraints Figure 1.6 dding the Solver constraints Set to max Select the Simplex LP method Figure 1.7 Solution found by Solver

4 Figure 1.8 Sensitivity report from Solver Table 1.5 Opportunity cost of making one European shirt Resource Shadow price Resource required Opportunity cost otton.5 per m 2 7m Labour 2.5 per hour Total 11. Figure 1.9 dding a new product Figure 1.1 The sensitivity report after adding a new product

5 Table 1.6 Transportation data for Z oil company Depot Refinery Required P Q R S vailable ost per litre for delivery from refinery to depot S Table 1.7 n initial feasible solution 25 units delivered from to P The refinery costs used in step 2 Depot Refinery v 1 v 2 v 3 Required u 1 P u 2 Q u 3 R u S u 5 Dummy vailable The depot costs used in step 2 Lines help to show that no more can be added to a route Quantity that won t be delivered Table 1.8 The stepping stone method dd 35 to this route Subtract 35 from this route Depot Refinery v 1 (5) v 2 (7) v 3 (7) Required u 1 () P u 2 ( 3) Q u 3 () R u ( 2) S u 5 ( 7) Dummy vailable Subtract 35 from this route Negative shadow price so not optimal dd 35 to this route

6 Table 1.9 The optimal solution Depot Refinery v 1 (5) v 2 (6) v 3 (6) Required u 1 () P u 2 ( 2) Q u 3 () R u ( 2) S u 5 ( 6) Dummy vailable ny combination of R and D on this side of the line meets Goal 1 Figure 1.11 Goal Goal 2 Goals 1 and 2 met here Figure 1.12 Goals 1 and

7 1 8 Goal 3 This goal can t be met 6 2 Goal 2 Goals 1 and 2 met here Figure 1.13 Goals 1, 2 and Goal onstraint for cell G7 Figure 1.1 The Excel model for Example 1. Figure 1.15 Setting up Solver for the first iteration Minimize d 1 Include all deviational variables

8 d 1 = Figure 1.16 Solver results after first iteration Figure 1.17 Setting up second iteration of Solver d 1 = Minimize d 2 + Figure 1.18 Final iteration of Solver d 2 + =

9 Figure 1.19 Final result of the Solver analysis d 3 > so Goal 3 cannot be met. est solution is to produce 15 Regular shirts Table 1.1 Data for Question Low wattage High wattage Fitting (seconds) 2 3 Testing (seconds) 1 3 ontribution (pence) 5 7 Table 1.11 Details for Question 5 asic Deluxe Resin 1 kg 16 kg Glass Fibre Mat 3 m 5 m Profit 5 8 Table 1.12 Details for Question 6 ELEN PLUS ELEN SUPER No. of component 8 No. of component 2 3 No. of component 1 Manufacturing time (hours) 5 7 Figure 1.2 Solver output for Question 8(b) djustable ells Final Reduced Objective llowable llowable Name Value ost oefficient Increase Decrease Government bonds 2 1E+3.15 orporate bonds 5. 1E+3 FTSE 1 Stocks im Stocks 125 1E+3.2 onstraints Final Shadow onstraint llowable llowable Name Value Price R.H. Side Increase Decrease onstraint E+3 5 onstraint onstraint onstraint onstraint

10 Table 1.13 Data for Question 1 onstraints ell Name Final value Shadow price onstraint RH side llowable increase llowable decrease $D$ $D$ E $D$8 Oven E+3 17 $D$9 Restaurant Table 1.1 Delivery requirements for Question 12 Retail outlets Number of boxes London 53 Wales 35 NW 5 NE 5 SW Table 1.15 verage cost per box for Question 12 Destination Warehouse London Wales NW NE SW Wat irm ri Table 1.16 Data for Question 13 Warehouse berdeen ristol olchester No. of containers required P Q * 8 35 R S No. of containers available *For operational reasons it is not possible to deliver to warehouse Q from berdeen