Market research indicates that consumers will buy x thousands of units of a particular kind of coffee markers when the unit price is: p(x)=-0.27x + 51 dollars. The cost of producing the x thousands units is C(x)=2.23x^2 + 3.5x +85  A. How much revenues R(x) and profit P(x) are obtained from producing x thousands of units (coffee markers)?  B. For what values of x is production of the coffee marker profitable?  Note: For part b of this question, please provide a detailed explanation and show your work

Suppose the weekly cost C, in dollars, of eliminating p percent of the pollution from the emissions of a factory is given by the following. C(p) = 5600p/100-p   (a) What type of function is this? (multiple choice) A. rational function B. identity function C. linear function D. polynomial function E. power function   (b) Given that p represents the percent of pollution removed, what is the domain of C(p)? (Enter your answer using interval notation.)   (c) Find C(0). (multiple choice) Interpret its meaning. A. The factory will gain revenue if no pollution is removed. B. There is no cost if no pollution is removed. C. Removing all the pollution will have a large cost. D. Removing all the pollution will have no cost. E. Even if no pollution is removed, there will be some cost.   (d) Find the weekly cost (in dollars) of removing 99% of the pollution. $ ?

Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =