PMLinear programming, solution

Can anyone help me with the solution of this problem please? Question 2 – Linear Programming (Maximise Contribution) The instruments department of Max Ltd makes two products: the XL and the YM. Standard revenues and costs per unit for these products are show below: XL TM $ $ $ $ Selling price 200 180 Variable costs: Material A ($10 per kg) (40) (40) Direct labour ($8 per hour) (32) (16) Plating ($12 per hour) (12) (24) Other variable costs (76) (70) (160) (150) Fixed overheads (allocated at $7 per direct labour hour) (28) (14) Standard profit per unit 12 16 Plating is a separate automated operation and the costs of $12 per hour are for plating materials and electricity. In any week the maximum availability of inputs is limited to the following: Material A 120 kg Direct labour 100 hours Plating time 50 hours A management meeting recently considered ways of increasing the profit of the instrument department. It was decided that each of the following possible changes to the existing situation should be examined independently of each other. (1) The selling price of product YM could be increased. (2) Plating time could be sold as a separate service at $16 per hour. (3) A new product, ZN, could be sold at $240 per unit. Each unit would require the following: Material A 5 kg Direct labour 5 hours Plating time 1 hour Other variable costs $90 (4) Overtime could be introduced and would be paid at a premium of 50% above normal rates. Required: (a) Formulate a linear programme to determine the production policy which maximizes the profits of Max Ltd in the present situation (i.e. ignoring the alternative assumptions in 1 to 4 above), solve, and specify the optimal product mix and weekly profit. (10 marks) (b) Determine the maximum selling price of YM at which the product mix calculated for requirement (a) would still remain optimal. (4 marks) (c) Show how the linear programme might be modified to accommodate the sale of plating time at $16 per hour (i.e. formulate but do not solve). (3 marks) (d) Using shadow prices (dual values), calculate whether product ZN would be a profitable addition to the product range. (5 marks) (e) Ignoring the possibility of extending the product range, determine whether overtime working would be worthwhile, and if so state how many overtime hours should be worked. (3 marks)