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A factory makes 3 components, A, B and C using the same production process for each. A unit of A take 1 hr, a unit of B takes 0.75 hrs and a unit of C takes 0.5 hrs. In addition, C has to be hand finished, an activity taking 0.25 hrs per unit. Each week total production time (excluding hand finishing) must not exceed 300 hrs and hand finishing must not exceed 45 hrs.
The components are finally assembled to make two finished products. One product consists of 1 unit of A and 1 unit of C selling for 30 pounds whilst the other consists of 2 units of B and 1 unit of C and sells for 45 pounds. At most 130 of the first product and 100 of the second product can be sold each week.
3. a. Formulate the problem of planning weekly production to maximize total proceeds as a linear programming problem in 2 variables and obtain the solution graphically.
3. b. Revise the price for the first product from £30 to £35 and resolve the problem graphically to find out and show the new optimum solution. Compare the old and new solutions with respect to the impact of the price.
3. c. Revise the limit for the number of the second product from 100 to 120 and resolve it graphically to find out and show the new optimum solution. Compare the old and new solutions with respect to the impact of the capacity limit.
3. d. Solve the problem with MS Excel Solver in-built functionality for all three cases to verify your solutions found graphically.