CIMA Revision Cards: Decision Management (CIMA Revision by Jo Avis

By Jo Avis

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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.

Calculate the NPV of each replacement cycle 2. Convert each NPV into an annualised equivalent 3. Choose the optimum cycle, based on the best AE 55 ————————————————————————————————————————— Investment Appraisal Capital rationing PI ¼ 2. 3. Assumptions KK Occurs when a company has limited investment funds and not all positive NPV projects can be adopted. Method: 1. Calculate the Profitability Index of each project. B. In the real world, a number of variables may alter at the same time. Probabilities may be used to predict the likelihood of various outcomes occurring Estimates – risk Methods that can be used to account for risk within a project appraisal include: KKKKKK 1.

0000 x2, x3, x4 ! 0000 Assembly: 5x1 þ 4x2 þ 3x3 þ 2x4 Finishing: 1x1 þ 4x2 þ 5x3 þ 3x4 Max production: x1 þ x2 þ x3 þ x4 9000 4950 1800 30 ————————————————————————————————————————— ––––––––––––––––––––––––––––––––––––––––––– Linear Programming Simplex K Relative loss Optimal production plan specifies no ornate tables. To make one would reduce contribution by £48 Worth K Optimal plan is to make 950 A, 250 B, 600 C and no D tables Total contribution earned would then be £168,750 Constraints 1 (cutting) and 3 (finishing) are binding Constraint 2 (assembly) will have 1450 spare hours Constraint 4 (max number) has been met exactly Constraint 5 (min number) has been exceeded by 150 units K KK K KK K The solution should be interpreted as follows: Constraints 1 and 3 are binding.

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