Question 3 (6 marks). Three products are made on 3 machines. Each of the products needs to be processed on each of the three machines. Each unit of the products can be sold for $3, $5, & S6, respectively. The machine capacities are 150 mm, 70 min & 100 min, respectively. The processing times are as follows. . Processing one unit or Product 1 requires 12 minutes on Machine 1, 6 minutes on Machine 2. & 8 minutes on Machine 3. Similar processing one unit of Product 2 requires 15 minutes on Machine 1, 3 minutes on Machine 2. & 12 minutes on Machine 3. Finally, processing one unit of Product 3 requires 16 minutes on Machine 1. 2 minutes on Machine 2 & 14 minutes on Machine 3. For some reason, it is required that Machine 1 runs at least 110 minutes a) Formulate the problem. You can write it in LINDO or LINGO format if you wish. NOTE Clearly define the variables. (b) Solve the problem with LINDO O LINGO What is the optimal production plan & what is its associated profit? (Write this as a sentence, don't just insert a printout) ) How many minutes of processing time are used on the three respective machines? (d) Explain the reduced cost (opportunity cost) of Product 1 Explain the dual price (the shadow price) of Machine 3 ( What would happen, if the minimum requirement of run time on Machine 1 (now 110) is increased to 1202