CAN YOU PLEASE FORMULATE THIS PROGRAMME, DONT SOLVE IT PLEASE FORMULATE THE PROGRAMME, WITH THE AVAILABLE INFORMATION.

8. Cornwall has been experiencing electricity shortages. The UK government is going to invest 1 billion (1 billion is 1000 million) over the next five years in an attempt to solve the Cornwall power shortage problem. It can invest in two types of power plants: Nuclear (N) and Hydroelectric (H). Every 1,000,000 invested into nuclear plants results in n megawatts capacity in two years (i.e. it takes two years to complete a nuclear plant). Every 1,000,000 invested into hydroelectric plants results in h megawatts in three years (i.e. it takes three years to complete a hydroelectric plant). A plant, regardless of type requires an operating budget in order to run. This operating budget makes up 20% of the cost of the plant. Operating budgets can only be used to keep the plant operational and cannot be used to start up new investments. However money from operating budgets and any surplus money can be invested into money markets (i.e. deposited into savings accounts at commercial banks) to accrue an interest at a rate of 10% per annum. In terms of power capacity, the UK currently has 50 megawatts of capacity and it can conserve energy to keep the demand at about 50 megawatts in the next two years. However, it needs 66, 70 and 78 megawatts of power in the third, fourth and fifth years respectively. Assume that once a plant is operational, it is always operational. Write down the linear program formulation that meets the increasing power demand and maximises the cash available to the UK government at the end of the fifth year. [ Total: 20 marks]