Please do part c and d

2. A manufacturing company produces units of product 1 and 22 units of product 2 per day. Product 1 makes a profit of 10 per unit, and product 2 makes a loss of 1 per unit. The total combined demand for the two products is 500 units per day, and the total demand for product 2 specifically is 100 units per day; the company must produce enough to meet this demand. One unit of product 1 uses 1 kg of resource A and 4 g of resource B; one unit of product 2 uses 3 kg of resource A and 1 g of resource B. There are a total of 2100 kg of resource A and 2200 g of resource B available each day. This leads to the company attempting to solve the linear programming problem: Maximise z = 1021 - 22 subject to x1 + x2 > 500 units; total demand 22 > 100 units; specific demand for product 2 2 +3.0, 0. (a) Solve the linear programming problem using the graphical solution method, and report the optimal number of units of products 1 and 2 to produce each day, along with the profit. (5 marks] (b) A global shortage occurs in resource B, which means that only (2200 - A) g are available each day (for some A > 0). At the same time, this shortage increases demand, because your competitors are unable to produce enough of their own products. This leads to the total demand for the products increasing to 500 + 2A. (The specific demand for product 2 remains unchanged, as do the profits per unit product.) Using your graphical solution, determine how your profit changes per unit A (for A comparatively small), and for what range of A this is valid. [5 marks] (c) Solve the linear programming problem again, this time using the two-phase simplex method. (Hint: at some point, you may have a choice between entering 11 or entering 14. It will be faster to enter 11.) [5 marks] (d) By considering carefully how our method for calculating shadow prices extends to this situation, answer (b) using your simplex tableaux, without any reference to the graphical solution. You must explain your method. [5 marks]