2. A coffee shop has the following fixed costs per month: $1,800 rent and utilities and...

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2. A coffee shop has the following fixed costs per month: $1,800 rent and utilities and $1,000 for employee wages. The average cup of coffee costs $0.21 in materials. The average price charged for a cup of coffee by the coffee shop is $2.30. (a) Define your input variable as a complete sentence. (b) Write the cost function, C(x). (c) Write the revenue function, R(x). (d) Find the profit function, P(x). Show your work and simplify completely. (e) Graph the cost and revenue functions with the window x: 0 to 2000 scl: 100 - 3000 to 4000 scl 200. (f) What is the significance of the point where the cost and revenue functions intersect? Write explanation as a complete sentence. (g) Find the intersection graphically and write as an ordered pair. What is the practical meaning of this point in the context of the situation? Write as a complete sentence. (h) If the coffee shop sells 1,000 cups of coffee in a month, is the company losing money or making money? (i) Use the profit function to determine how much money the company will lose or make if they only sell 1,000 cups. () Graph the profit function using the same window as above. Looking at the graph of the profit function, where is the breakeven point? What is the profit at the breakeven point? (k) The value of the input at this point is called a zero of the function. What can we say about the profit function for input values lower than the breakeven point? What can we say about input values that are higher than the breakeven point? 2. A coffee shop has the following fixed costs per month: $1,800 rent and utilities and $1,000 for employee wages. The average cup of coffee costs $0.21 in materials. The average price charged for a cup of coffee by the coffee shop is $2.30. (a) Define your input variable as a complete sentence. (b) Write the cost function, C(x). (c) Write the revenue function, R(x). (d) Find the profit function, P(x). Show your work and simplify completely. (e) Graph the cost and revenue functions with the window x: 0 to 2000 scl: 100 - 3000 to 4000 scl 200. (f) What is the significance of the point where the cost and revenue functions intersect? Write explanation as a complete sentence. (g) Find the intersection graphically and write as an ordered pair. What is the practical meaning of this point in the context of the situation? Write as a complete sentence. (h) If the coffee shop sells 1,000 cups of coffee in a month, is the company losing money or making money? (i) Use the profit function to determine how much money the company will lose or make if they only sell 1,000 cups. () Graph the profit function using the same window as above. Looking at the graph of the profit function, where is the breakeven point? What is the profit at the breakeven point? (k) The value of the input at this point is called a zero of the function. What can we say about the profit function for input values lower than the breakeven point? What can we say about input values that are higher than the breakeven point?