Hello, I am trying to understand how to solve this question and this is all the information that was provided for the question on the past paper. What could I do to solve it with this information?

Question 7: a) Crazy Rugs own 100 glorious Persian rugs which must be sold in the next two peri- ods (period I and period 2). Buyers in each period will pay for their purchases at the end of the period. The undiscounted profit functions for sales in period one and two are given by: 7(q) = 50q - 0.5(71)2 (7) "(41) = 5092 - 0.5(92)' (8) Using the method of lagrange calculate the quantities that should be sold in each period supposing that profits are discounted at a rate of 25% per period. (6 marks) b) A mining company must consider between two strategies for mining its resource. By investing $10 million now, it can make a net profit earned at a constant rate of 83 Million per year for 10 years, at which time the resource will be exhausted. Alternatively, the company can invest $15 Million now to obtain a net profit of 85 Million per year for 7 years. Assuming a nominal discount rate of 10% compounding continuously, which gives the highest NPV for the exploitation of the resource. SHOW your WORKING. (4 marks)