A company produces two types of products, Product A and Product B, using two machines, Machine X and Machine Y. Each unit of Product A requires 3 hours on Machine X and 2 hours on Machine Y, while each unit of Product B requires 1 hour on Machine X and 4 hours on Machine Y. The company has 120 hours available on Machine X and 100 on Machine Y per week. Additionally, the company must satisfy the following constraints: The company cannot produce more than 50 units of Product A per week. The profit per unit of Product A is $50, and the profit per unit of Product B is $40. The company wishes to determine how many units of each product to produce weekly to maximize total profit. a) Use Python to solve this problem, and make sure your answer is consistent with part b. Also, report the sensitivity analysis parameters such as slack and shadow prices for all constraints. b) What constraints are binding? Interpret the shadow price value of each constraint.