Neco 2019 Agricultural Science Question 19

A farmer has a \(10\) ha maize field. The proportion of plants infected by a fungal disease after \(t\) weeks is modeled by \(I(t)=\frac{1}{1+e^{-0.5(t-4)}}\). A fungicide application instantly reduces the infected proportion by \(30\%\) of its current value and can be applied at most twice, at weeks 3 and 6. The yield loss at harvest (week 12) is \(0.05\) t/ha per 1 % increase in final disease incidence. Maize price is \(\text{₦}200\) per kg and the expected yield without disease is \(10{,}000\) kg/ha. Fungicide costs \(\text{₦}15{,}000\) per application. Determine the optimal spraying schedule (which weeks to spray) that minimizes the total cost (fungicide cost plus value of lost yield) and state the minimum total cost.