Science:Math Exam Resources/Courses/MATH100 C/December 2023/Question 28/Statement

Doctor Roberts considers starting up a new factory making umbrellas. The factory would have fixed costs of $5,000 per month and each umbrella would cost $8 to produce. Market research indicates that if ${\textstyle x}$ thousand umbrellas are produced every month, they can be sold at price ${\textstyle p(x)=30-x}$ dollars. Determine the optimal profit per month and the production level at which it occurs. Give units for your answers.