part (ii) and (iv)

this is quite literally the entire question. the white gap is a page break

Recently engineers have become involved in the area known as waste minimization. As one example, the operation of a chemical plant may be optimized so that its impacts on the environment are minimized. Suppose a refinery develops a product 21 made from two raw materials X and Y. The production of 1 metric tonne of the product involves 1 tonne of X and 2.5 tonnes of Y and produces 1 tonne of liquid waste W. The engineers have come up with three alternative ways to handle the waste: 1. Produce a tonne of a secondary product Z2 by adding an additional tonne of X to each tonne of W. 2. Produce a tonne of another secondary product Z3 by adding an additional tonne of Y to each tonne of W. 3. Treat the waste so that it is permissible to discharge it. The products yield profits of $2500,-$50, and $200 /tonne for 21, 22, and Z3, respectively. Note that producing Z2 actually creates a loss. The treatment process costs $300 /tonne. In addition, the company has access to a limit of 7,500 and 10,000 tonnes of X and Y, respectively, during the production period. Determine how much of the products and waste must be created in order to maximize profit. Obtain the solution: (i) Graphically. (ii) Using the Simplex method (i.e., by hand, using pen and paper and calculator, or equivalent; do not code). (iii) Using the Simplex LP method available in the Solver tool in Excel. (iv) Using the linprog function in Python