In a specific project, ground water level has to be reduced prior to construction and $3$ specific well locations have been chosen. The steady state water level $($h$)$ at the most critical point can be expressed as a function of pumpage rates $(Q_i)$ at these locations.

$h=1\mathrm{.}0+(0\mathrm{.}7**Q_1+1\mathrm{.}4**Q_2+1\mathrm{.}0**Q_3)$

The cost of each well is composed of an initial cost and operating costs $($function of discharge$)$

$COS{T}_1=30+12**Q_1$

$CoS{T}_2=45+10**Q_2$

$COS{T}_3=38+11**Q_3$

Formulate a mathematical program that will determine the optimal $($cost efficient$)$ well discharges if maximum pumpage rate is limited to $3\frac{m^3}{sec}$ for each well and the desired steady state level is $8\mathrm{.}0$ m $.$

$($Note : Make sure that no initial cost is applicable for a well with zero discharge$).$