please answer all parts.

2} Imagine a rm that has the following production flmction: y =I132 Note that this implies the following marginal products (Note very carefully the sub scripts. They are not a mistake). MP1 =32 MP2=171 Note that this question can be tricky if you tr_',r to do it too quickly. If you are having trouble, try at least showing what is happening graphically and explain the intuition. This will get you some good part marks. a) (5 marks} Suppose the price of input 1 was equal to $5, and the price of input 2 was equal to fill]. What would he the optimal inputs for this rm if it wished to produce 450 units of output? Hint use the optimality ratio from having the slope of the isooost equal the slope of the isoquant. Combine this with the production function and you should get your answers. The numbers will be nice whoie numbers. In} (5 marks) Suppose the price of input 1 increased to $20. 1What would he the optimal inputs for this rm if it still wished to produce 450 units of output? You can use the same approach as the last question. c) (5 marks) Explain how the rm responded to this increase in price, and how its total costs changed as a result