NAME $$ General Education $-$ Chapter $4$

General Education Assignment Instructions: Save your assignment as a single pdf file $($not a file for each page of your document and not in other formats$),$ see the video under Content on the D$2$L or send the instructor an email if you have any issues saving your file as a pdf$.$ Clearly communicate your answer explaining$/$justifying each step in your response and show your work.

A company determines that its marginal revenue is given by

$R^{\text{'}}(t)=3t^2-24t40$ with $R(0)=0$

when $0t50.$ The company's marginal cost is given by

$C^{\text{'}}(t)=50t$ with $C(0)=500$

when $0t500.$ Find $P(50).$