# Having trouble with this Calculus word problem involving Demand, Cost, Revenue, Profit

The 2 variables are messing with my head. Please help me make sense of this? I can't even get it set up right and I'm ready to throw my notebook out a window. Thanks in advance! Problem below:

The demand x for a certain product can be modeled by x = 100e^-0.02p per week.

The cost of supplying each unit is $25. a) Write the PROFIT function as a function of price p b) What is price p at which the maximum profit is realized? ## 1 Answer The demand $$x$$ is a function of the price $$p$$: $$x = 100e^{-0.02}p$$ The profit per item is the price less the cost: $$p-25$$ and $$x$$ items are sold. Can you continue from here? • ok, so Profit = x(p-25), or (100e^-002p)(p-25) ? – Mahzsa May 5 at 22:07 • Yes, that's right. You need to put $ signs around the MathJax for the formatting commands to take effect. Take a look at how I edited your question. – saulspatz May 5 at 22:50
• Thank you for the help. I think I was a bit brain fried, it looks obvious to me now. Part b I found the derivative and critical number to determine the max profit. – Mahzsa May 5 at 23:40