Need help with STRATEGIC LOGISTICS questions

Sample Question: A transportation company needs to decide how many small, medium, and large trucks to purchase. Each small truck has a purchase price of £15000, costs £2500 a year to run, and can transport an average of 1000 items per day. Each medium truck has a purchase price of £25000, costs £3200 a year to run, and can transport an average of 2000 items per day. Each large truck has a purchase price of £40000, costs £4000 a year to run, and can transport an average of 4000 items per day. The company has the following strategic goals: Goal 1: Do not spend more than £750,000 on the initial purchase of all the trucks Goal 2: Keep the total annual running costs of all the trucks below £60,000 Goal 3: Maintain a transportation capacity of at least 50,000 items per day Goal 4: Have a fleet of exactly 30 trucks. Additionally, the company needs to ensure that at least 50% of its trucks are either small or medium size. (a) Formulate (but do not solve) a weighted goal programme whose solution will tell the company how many of each truck size to purchase. You may assume all four goals are of equal importance. (b) Give the achievement function of a lexicographic goal programme which will prioritise the goals in the following criterion order: Annual running costs, transportation capacity, fleet size, initial purchase cost. (c) Give the alterations and additions needed to your model from part (a) in order to formulate a Chebyshev goal programme where all goals are of equal importance.