3 SECTION A: OPTIMISATION 5 Question A1 [5 marks] 5 7 A company makes wooden garden chairs and benches. Their objective is to maximise profit. The profit on each chair is £47 and on each bench is £37. 3. 9 Each chair requires 9 units of materials, 5 units of machine time and 6 units of labour. D Each bench requires 8 units of materials, 7 units of machine time and 4 units of labour. 1 The resources available are 4000 units of materials, 3400 units of machine time and 2600 units of labour. 2 B Let x be the number of chairs made and y be the number of benches made then 7 the inequalities governing the resources will be 9x+8y ≤ 4000, 5x + 7y ≤ 3400 and 6x + 4y ≤ 2600. 5 5 The objective function, P, is given by P=ax+by where a and b are constants. 7 3. 1) State the value of b 9 , When 130 chairs and 230 benches are made, work out/n1) State the value of b When 130 chairs and 230 benches are made, work out 2) the amount of materials used, 3) the profit. Now use Solver to find the optimal solution to the problem. NOTE: you will not be able to run Solver within this WATS worksheet. You will need to use a different Excel worksheet, for example, the Templates provided for the lecture. For this optimal solution state: 4) the maximum profit, 5) the number of benches made. to nearest pound to 1dp/nQuestion A2 [6 marks] A company makes ornamental plates and vases. Their objective is to maximise profit. The profit on each plate is £3.00 and the profit on each vase is £3.30. Let x be the number of plates made and y be the number of vases made. The materials required are 4 units for a plate and 7 units for a vase. The labour required is 26 units for each plate and 15 units for each vase. The resources available are 5000 units of materials and 22000 units of labour. The constraint for materials is cx + dy ≤ 5000 where c and d are constants. State the values of 1) c 2) d 3) Decide whether the following statements are TRUE or FALSE. First "For a solution to our practical problem x can be positive, negative or zero." Second "There are 2 inequalities which form the boundaries of our feasible region."/n3) Decide whether the following statements are TRUE or FALSE. First "For a solution to our practical problem x can be positive, negative or zero." Second "There are 2 inequalities which form the boundaries of our feasible region." If you think: First Second then Enter TRUE TRUE 1 TRUE FALSE 2 FALSE TRUE 3 FALSE FALSE 4 (1, 2, 3 or 4) Now use Solver to find the optimal solution to the problem. NOTE: you will not be able to run Solver from within the WATS worksheet. You will need to use another Excel worksheet to find the optimal solution, for example, th For your optimal solution state: to nearest pound 4) the maximum profit, 5) the number of vases made, to 1dp 6) the amount of labour used. to 1dp

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3 SECTION A: OPTIMISATION 5 Question A1 [5 marks] 5 7 A company makes wooden garden chairs and benches. Their objective is to maximise profit. The profit on each chair is £47 and on each bench is £37. 3. 9 Each chair requires 9 units of materials, 5 units of machine time and 6 units of labour. D Each bench requires 8 u