A plastic product manufacturer produces two types of products, Juara and Johan. The manufacturer needs 20 kg of material A, 10 litres of chemical B, and 1 hour of processing time to produce one unit of Juara. On the other hand, It requires 10 kg of material A, 15 litres of chemical B, and 1 hour of processing time to produce one unit of Johan. Due to high demand on both products, the manufacturer must at least produces 2 units of Juara and 2 units of Johan each day. The total daily supply of material A and chemical B are 200 kg and 150 litres respectively. The manufacturer has a maximum of 12 hours processing time a day. The net profit obtained from selling the Juara is $ 11 per unit and that Johan is $ 14 per unit.

a) Formulate this problem if the objective of the manufacturer is to maximize the net profit.

b) Solve the problem graphically, and find how many each products to be produced, and what is the amount of daily net profit obtained.

c) Identify and list down the binding and non-binding constraints.

d) If the daily supply of material A is now available for one extra kg, using sensitivity analysis to find the shadow price for this extra kg of material A, and give your comment to the manufacturer if the cost of obtaining the extra kg of material A is $ 1.