Instruction: Given the word problems below, convert them into linear programming models, i.e, convert into equivalent numerical models, transform into standard form and graph the solution space of the variables.

1. A small firm builds two types of garden shed. Type A requires 2 hours of machine time and 5 hours of craftsman time. Type B requires 3 hours of machine time and 5 hours of craftsman time. Each day there are 30 hours of machine time available and 60 hours of craftsman time. The profit on each type A shed is 60 and on each type B shed is 84. Formulate the appropriate linear programming to maximize profit.

2. A farmer has 20 hectares for growing barley and swedes. The farmer has to decide how much of each to grow. The cost per hectare for barley is 30 and for swedes is 20. The farmer has budgeted 480. Barley requires 1 man-day per hectare and swedes require 2 man-days per hectare. There are 36 man-days available. The profit on barley is 100 per hectare and on swedes is 120 per hectare. Find the number of hectares of each crop the farmer should sow to maximise profits.

3. A firm manufactures wood screws and metal screws. All the screws have to pass through a threading machine and a slotting machine. A box of wood screws requires 3 minutes on the slotting machine and 2 minutes on the threading machine. A box of metal screws requires 2 minutes on the slotting machine and 8 minutes on the threading machine. In a week, each machine is available for 60 hours. There is a profit of 10 per box on wood screws and 17 per box on metal screws. Formulate this problem as a linear programming problem given that the objective is to maximise profit.