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**Extra info for CIMA Revision Cards: Decision Management (CIMA Revision Cards)**

**Example text**

The number of units of B produced must be double the number of units of A x1 þ x2 ! 20 x1 100 Feasible region 80 Constraints 60 K x2 ! 2x1 Products A and B must be manufactured in the ratio 2 : 7 7x1 ¼ 2x2 A,B,C,D,E - extreme points 40 20 A E B C D 20 40 x2 60 80 100 27 ————————————————————————————————————————— Linear Programming Slack and surplus The optimal solution can be used to determine which of the constraints are binding. Insert the amounts to be produced of each unit into each constraint Surplus is concerned with ‘greater than or equal to’ constraints Production > Minimum required ) surplus created Example Where a constraint is binding, obtaining more of it would increase contribution Optimal solution is 10u of x, and 28u of x2 For constraint 3x1 þ 10x2 330, insert the solution: 3(10) þ 10(28) ¼ 310 Slack/surplus can then be calculated 330 À 310 ¼ 20 slack Slack is concerned with ‘less than or equal to’ constraints Usage < Amount available ) slack available 28 ————————————————————————————————————————— ––––––––––––––––––––––––––––––––––––––––––– Linear Programming Shadow prices and opportunity costs Definition Shadow price is the increase in value that one extra unit of a limiting resource would create.

G. A technique for allocating scarce resources between products to maximise the benefit from them when there is more than one limiting factor Let x2 ¼ no. of units of product B made 2. Study tip 3. Let x1 ¼ no. g. g. Machine hours 3x1 þ 10x2 330 Where a unit of A takes 3 hrs to machine, a unit of B takes 10 hrs and the total hours available are 330 4. g. Product A x1 ! 0 1. e. g. g. K 5. Draw 2 axes Plot all the constraints as straight lines Identify and mark the feasible region Determine the values of the decision variables at the extreme points of the feasible region and, for each, the corresponding value for the objective variable Choose the largest answer (maximisation) or the smallest (minimisation) Total combined output of products A and B must be at least 20 units K 1.

Insert the amounts to be produced of each unit into each constraint Surplus is concerned with ‘greater than or equal to’ constraints Production > Minimum required ) surplus created Example Where a constraint is binding, obtaining more of it would increase contribution Optimal solution is 10u of x, and 28u of x2 For constraint 3x1 þ 10x2 330, insert the solution: 3(10) þ 10(28) ¼ 310 Slack/surplus can then be calculated 330 À 310 ¼ 20 slack Slack is concerned with ‘less than or equal to’ constraints Usage < Amount available ) slack available 28 ————————————————————————————————————————— ––––––––––––––––––––––––––––––––––––––––––– Linear Programming Shadow prices and opportunity costs Definition Shadow price is the increase in value that one extra unit of a limiting resource would create.