Formulate but do not solve the following as an LP.

A 50 acre orchard in Kelowna was released from the Agricultural Land Reserve and sold to the city for the development of parks, high density housing, and municipal office buildings. The city has a budget of $ 7.6 million for initial development and this amount cannot be exceeded by law. There is an initial (non-annual) cost of $ 3,000 per acre for parks that comes out of the development budget. Each acre of park requires 28 hours of municipal workers time for maintenance per year. Moreover, each acre of park generates an annual net profit of $70 per acre. For high density housing, there is an initial cost of $200,000 per acre for development, and a requirement of 4,000 hours of municipal workers time per acre to maintain annually. The high density housing is for low income tenants and so only generates an annual net profit of $1,500 per acre. Each acre developed for municipal office buildings costs $180,000 for initial development, provides office space for 56 municipal workers while requiring 300 hours of municipal workers time to maintain annually. Each of the 70 municipal workers provides 1920 hours of work per year, and each worker requires their own office space provided by the municipal office development. Set up an LP (but do not solve) that could be used to determine the number of acres allocated for each type of development in order to maximize the annual net profit generated by the entire project while meeting the project's requirements. Make sure to define your decision variables precisely and to provide a descriptive label for each constraint.

 

b) Consider the following development plan: [9 Marks] parks: 3.1 acres high density housing: 31.7 acres municipal office buildings: 2.5 acres Using the LP set up in (a) and this plan, answer the following: 

i. How many maintenance hours does the plan require? ii. Verify that the plan is a feasible solution to your LP. iii. What is the net profit of this plan? iv. By trial and error, find a new feasible solution that has more net profit by changing only one of the values of the plan given in (b) while leaving the other two values the same. Next, by changing only this same value, determine, with explanation, the feasible solution with the most net profit possible.