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Additional info for ACCA F5
A 8x + 10y = 11,000 b 4x + 10y = 9,000 4x = 2,000 x = 500 y = 700 (a – b) Therefore the optimal product mix is to make and sell 500 units of X and 700 units of Y. The maximum contribution is (500 x 4 + 700 x 8) = £7,600. This can be checked by seeing how much of the constraints are used up: Dept hours used hours available A 500 x 8 + 700 x 10 = 11,000 hours 11,000 hours B 500 x 4 + 700 x 10 = 9,000 hours 9,000 hours B 500 x 12 + 700 x 6 = 10,200 hours 12,000 hours Slack and surplus Departments A and B are fully utilised or what are termed binding constraints (ie they bind the decision or output).
Define the problem Let x = number of units of R produced Let y = number of units of S produced 2. org 51 C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R PR O GR A M M I N G 3. Subject to – constraints (Dept A hrs) 8x + 10y ≤ 11000 (Dept B hrs) 4x + 10y ≤ 9000 (Dept C hrs) 12x + 6y ≤ 12000 (non-negativity) x, y ≥0 4. Plotting the graph If we know the constraints we are able to plot the limitations on a graph identifying feasible and non-feasible regions. The linearity of the problem means that we need only identify two points on each constraint boundary or line.
If the components are sub-contracted, the company will have spare capacity. How should that spare capacity be profitably used, that is, are there hidden benefits to be obtained from sub-contracting? 2. Would the sub-contractor be reliable with supply and delivery time? 3. Would the sub-contractor supply the same or improved quality components as the one produced internally? 4. Does the company wish to be flexible and maintain better control over operations by making everything itself? 5. The going concern of the sub-contractor should also be considered.