I have no idea how to do this, I tried a lot of things but they don't make sense and I have too many variables.
A manufacturer has been selling lamps at the price of \$6/lamp, and at this price they have been selling 3000 lamps a month. The manufacturer wishes to raise the price and estimated that for each \$1 increase they will sell 1000 fewer lamps a month. The manufacturer can produce the lamps at a cost of \4 per lamp Express the manufacturers monthly profit as a function of the price that the lamps are sold, draw the graph and estimate the optimal selling point.
I think the profit should be \#(\mathrm{lamps\ sold})\cdot(\mathrm{price\ of\ lamps}) - 4\cdot\#(\mathrm{lamps\ sold})$.