Pizza and Break-even Point Essay

Complete both parts. a) What are the three methods used for solving systems of equations? Which method do you prefer to use? b) Break-Even Analysis – Systems of Equations Application Problem Suppose a company produces and sells pizzas as its product. Its revenue is the money generates by selling x number of pizzas. Its cost is the cost of producing x number of pizzas. Revenue Function: R(x) = selling price per pizza(x) Cost Function: C(x) = fixed cost + cost per unit produced(x). The point of intersection on a graph of each function is called the break-even point. We can also find the break-even point using the Substitution Method. Suppose Dan’s Pizza Parlor has a fixed cost of $280 and it costs $4 to produce each pizza. Dan sells every pizza for $12. The Revenue Function is: R(x) = 12x The Cost Function is: C(x) = 280 + 4x The break-even point occurs where the graphs of C and R intersect. Therefore, we can find this point by solving the system: y =12x y = 280 + 4x. How many pizzas does Dan have to produce to break-even? If he exceeds his break-even point, will he make a profit or have a loss? A) What are the three methods used for solving systems of equations? Which method do you prefer to use? graphing, substitution, and elimination. I use all there but I think I use elimination more. B) C(x) = 280 + 4x r(x)= 12x 12x= 280 + 4x 8x=280 x= 35 R(x) =12(35) =$420 So Dan has to produce 35 pizzas to produce his break-even point. He will have a$420 profit.