A small co-operative craft workshop makes two types of table : a standard rectangular table and a deluxe circular table. The market can absorb as many of either types of table as the workshop can product, so we can assume unlimited demand. Each type of table is made from the same wood and once the wood has been cut, each table has to go through 3 processes : joinery, pre-finishing and final finishing (in that order). Sufficient cut wood is always available. Each rectangular tables takes 2 hours for joinery, 40 minutes for pre-finishing and 5 hours 20 minutes for final finishing. Each circular table requires 3 hours for joinery, 2 hours for pre-finishing, and 4 hours for final finishing. The workshop employs five joiners, two sanders and eight polishers. The joiners each work a fixed six-hour day while the sanders and polishers each work a fixed eight-hour day on the pre-finishing and final finishing respectively. No overtime is worked and full six-hour or eight-hour days are worked by each employee irrespective of whether there is work for that employee to do. All running costs, including wages are fixed. The co-operative sells each rectangular table for €120 and each circular table for €150. How many of each type of table should the workshop produce each day in order to maximise its profit? Formulate this linear programming problem.
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