[Question 1] (The total marks available for this question is 20. The weighting of each subpart is indicated in %.) A company owns a warehouse that can be used to store products of two types, type A and type B. The total storage space of the warehouse is 400 square metres. According to the existing regulations, the ratio of the space for storing type-A products to type-B products should be at least 3:2 but no more than 6:2. (Hint: The ratio of x to y is at least 3:2 if x/y ≥ 3/2.) (a) Suppose that the profits of storing type-A and type-B products are PÅ and PB pounds, respectively, per square metre allocated. The company wants to maximise the total profit. Formulate a linear programming model to identify an optimal allocation of space for storing these two types of products. [40%] (b) Use graphical constructions to analyse the model formulated in your answer to part (a). In particular, answer the following question: Is it possible to make a decision on an optimal allocation of space without knowing the exact values of PA and PB? (Hint: Start with considering the case of PA = PB-) [40%] (c) Assume now that the company can rent the space not unused for products of types A and B. It is estimated that this would yield a profit of c pounds per square metre of all space unused by the two types of products. Amend the linear model from your answer to part (a) by incorporating the possibility of getting the additional profit. [20%]