List and explain the three steps in formulating a linear programming problem. [10 Marks] Q 4(b) An electronics company produces two types of smartphones. The first, a low-end smartphone costs $2,500 per batch to produce. The second, the flagship model, costs $3,000 per batch. Based on an analysis of current inventory levels and outstanding orders, production manager has specified that at least 30 batches of the low-end model and at least 20 batches of the flagship model must be produced during the next month. In addition, the manager notes that an existing inventory of highly perishable raw materials needed in both phones must be used so, to avoid wasting the expensive materials, the company must produce a total of at least 60 batches of both smartphones. The problem is to minimise total cost of production. Formulate this as a linear programming problem, giving the three steps and state any assumptions (constraints) made. Q 4(c) [12 Marks] Solve the LP problem in Q4(b) graphically. Hence, state your recommendation for the number of batches of low-end and flagship models the company should produce in order to minimise the production costs. Give the total cost of manufacturing that would be expected given your solution. Q 4(d) [7 Marks] Suppose the problem of Q4(b) is extended to include a third brand of phone - mid- range, the making of which costs $2,800 per batch. It needs to be manufactured in at least 40 batches. Due to the limits of raw material supply, at least 90 batches of all phones must be produced together to avoid material wastage. Extend the formulation to this larger class of problems.