Operation Research with cplex program

A company produces two types of products, A and B. Each product has a different production cost and sells for a different price. The company has a budget of $10,000 to spend on production, and it can sell all the products it produces. The company wants to maximize its profit. The production costs and selling prices for each product are as follows: Product A: Production cost =$50, Selling price =$100 Product B: Production cost =$30, Selling price =$80 The company has the following constraints on its production: The company can produce at most 100 units of product A. The company can produce at most 200 units of product B. The company must produce at least 50 units of product A. 1) Formulate this problem as a linear programming model : 2) Solve it and perform sensitivity analysis on the model to determine the range of values for which the optimal solution remains the same using CPLEX. Upload your Cplex code to Blackboard cplex quiz. Optimal solution: Optimum objective function value: Optimality range: Feasibility range: 3) Use your sensitivity analysis results in Cplex to answer the following questions: A) What happens to the optimal solution if the budget constraint is changed from $10,000 to $12,000 ? B) What happens to the optimal solution if the maximum production constraint for product A is changed from 100 to 150 ? C) What happens to the optimal solution if the selling price for product B is increased to $100