15. Noah's Boats makes three different types of boats. All boats can be made profitably in this company, but the company's monthly production is constrained by the limited amount of labour, wood and screws available each month. The director will choose the combination of boats that maximises his revenue, in view of the information given in the following table:

(a) Formulate the above as a linear programming problem.

(b) Solve it by the simplex method.
From the optimal table of the solved linear programming problem, answer the following questions:
(

c) How many boats of each type will be produced and what will be the resulting revenue?

(d) Which, ifanY, of the resources are not fully utilised? Ifso, how much of spare capacity is left?

(e) How much wood will be used to make all of the boats given in the optimal solution?

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Input Row boat Canoe Kayak Monthly availability Labour (hours) 12 7 9 1,260 hours Wood (Board feet) 22 18 16 19,008 board feet Screws (kg) 2 4 3 396 kg Selling price (in Rupees) 4,000 2,000 5,000