BUS 111 Lecture 16: BUS111_0005_11-30-15
Document Summary
Often, these problems involve many functions of time e. g. revenue increases with number of clients, but clients change over time. This is going to give us (cid:498)mathematically speaking(cid:499): R(cid:523)x(cid:524) with x as a function of time, i. e. x= some formula with t"s in it. Write profit function : p(x)= r(x) c(x) P(x)=1000x-x2 (3000+20x) = 980x-x2-3000 problem, everything is done implicitly with a whatever/dt on all variables. Example: for jdt landscaping, the revenue from maintaining x homes is given by r(x)=1000x-x2 , and the cost is c(x)=3000 +20x. If the company has 400 clients now and is increasing the client base at a rate of 3 clients per month, how quickly is their profit increasing: dp/dt= 980dx/dt -2xdx/dt, dp/dt= 980(3) -2(400)(3) / month. The profit is increasing by each month. Steps: draw a picture, write equations, etc, differentiate implicitly with respect to time, plug in all known information, write it up.
