A multiple effect evaporator is to be used to evaporate $200,000kg$ of water per day from a fruit juice. The total initial cost of the first effect is $150,000TL,$ and each additional effect $100,000TL.$ The annual depreciation cost is $8\%,$ annual fixed charges are $18\%,$ and annual maintenance charges are $10\%$ of the initial cost of the evaporators. Steam costs $3$ TL per $100kg.$ All other costs are independent of the number of evaporators. The unit will operate $300$ days per year. The kg of water evaporated per $kg$ of steam $=0\mathrm{.}8N,$ where $N$ is number of evaporators. What should be $N,$ for minimum annual cost? Note that the annual cost$=$ annual depreciation cost $+$ annual steam cost $+$ annual maintenance cost $+$ annual fixed charges.

Latfen birini se$$in:

a$.5\mathrm{.}9$

b$.4\mathrm{.}9$

c$.3\mathrm{.}9$

d$.7\mathrm{.}9$

e$.2\mathrm{.}9$