A nursery planted deciduous and evergreen shrubs in an area of $30,000 \,\rm{m}^2$. An evergreen shrub requires $1 \,\rm{m}^2$ and a deciduous $2 \,\rm{m}^2$. The two types of shrubs have different climatic requirements, so that the number of the one type not to exceed twice the number of the other type. To be certain that good customers having reasonable orders will not exceed the number of shrubs, the number of deciduous was held between $7,000$ and $9,000$ plants, while the evergreen was delimited between $11,500$ and $14,250$. In addition, the nursery has long term contracts for a few years later, which require having any time requested $20,000$ bushes.
Unfortunately, evergreen shrubs require twice the attention the deciduous require while growing, so the nursery can only supply $36,000$ deciduous and $18,000$ evergreen shrubs or any possible combination of these two.
Until recently, the profit margin for deciduous shrubs was three times greater than that of evergreen, but some change in the market equated them. What effect will this change cause to the number of shrubs, if the manager of the nursery wants to maximize the total profit?
Im having hard time trying to figure out how to formulate the profit function, so that I could maximize it subject to the constraints, and even doubting whether it is actually even possible. Wouldn't I have to know at least what are the prices that the shrubs could be sold for?
If the numbers of deciduous shrubs is $d$ and the number of evergreen shrubs is $e$, then from the information about profit margins