The manager of a restaurant found that that the cost to produce 100 cups of coff
ID: 3191813 • Letter: T
Question
The manager of a restaurant found that that the cost to produce 100 cups of coffee is $11.02, while the cost to 400 cups is $40.12. Assume the cost C(x) is a linear function of x, the number of cups produced. A) Find the equation for C(x) B) What is the fixed cost? C) Find the total cost of producing 1000 cups of coffee. D) Find the number of cups of coffee produced when the total cost is $62.15. Round to zero deci8mal places. E) What is the slope of C(x) and interpret it in the words of the problem?Explanation / Answer
you have two data points: (100 , 11.02) and (400 , 40.12) slope between these points: (40.12 - 11.02) / (400 - 100) = 29.10 / 300 = .097 y = mx + b, and we know m = .097 using (100 , 11.02) as (x,y), we can solve for b 11.02 = .097(100) + b 11.02 = 9.70 + b b = 11.02 - 9.70 = 1.32 a) C(x) = .097x + 1.32 b) the fixed cost is the cost of 0 cups, or the y-intercept: $1.32 c) C(1000) = .097(1000) + 1.32 = $98.32 d) C(1001) = .097(1001) + 1.32 = $98.42 e) marginal cost = C(1001) - C(1000) = .097 (the slope, go figure!) f) the marginal cost of any cup is .097-- the slope what this means is that once the fixed cost is absorbed, the marginal cost of any cup is going to be the same, so keep on pumping them out to avoid having to pay the fixed cost again
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.