The Question.

The scenario

Park Furnishings manufactures school and university classroom furniture. The company has two production plants, located at Easton and Weston. The Easton plant produce tables and chairs and the Weston plant produces desks and computer workstations. Park has a working day of 7.5 hours and employs nine workers at each plant. You may assume that there is a total of 24 working days every month.

All Park products are manufactured using finished pressed wood and polished aluminium fittings. Including scrap, each table and desk uses 20 m² of pressed wood whereas each chair and workstation needs 12.5 m² and 30 m² respectively. A total of 75000 m² of pressed wood is available each month and is divided equally between the two plants. The aluminium fittings that reinforce the legs of all the production items are purchased from an outside supplier. Each plant can purchase up to 3000 boxes of fittings per month and one box is required for every item of furniture produced. Production times are 72 minutes per table, 18 minutes per chair, 90 minutes per desk and 2 hours per workstation.

The unit profit for chairs and tables are 31 and 77 respectively, whereas each desk and workstation generates profits of 108 and 132 respectively.

Park is considering combining operations of both plants into a single factory. This consolidation will have the advantage of combining all available production resources as well as reducing administration costs by 1700 per month; however they have estimated that the cost of renovating and equipping the factory will be 1300000. Due to the current financial position Park Furnishings is only prepared to go ahead with the combined operation if it saves money in the first year of operation.

Let

• x1x1 represent the number of tables made per month;
• x2x2 represent the number of chairs made per month;
• x3x3 represent the number of desks made per month;
• x4x4 represent the number of workstations made per month;

where x1,x2,x3,x40

(c) Combined Enter the constraints for combining the plants and the expression to be optimised. Maximise: O 2 + 12+ 13+ O n subject to O2+ O2z+ O2+ O2450 [Wood] O 21+0 2+O 23+ 245 [metal fittings] O 2 + O 2z+ 13+ O 2 0 (Labour] Determine the optimal solution for 21, 22, 23 and 24 and the profit that this solution will generate and enter your solution below. (Enter the optimal solution correct to 3dp and the profit to the nearest pound.) The optimal solution is x = 22=0 23= 0 14 = Profit: Is it economically sensible to combine the two plants? Select