Solve the problem.
-A bakery makes and sells pastries. The fixed monthly cost to the bakery is $770. The cost for labor, taxes, and ingredients for the pastries amounts to $0.90 per pastry. The pastries sell for $1.60 each.
a) Write a linear profit function representing the profit for producing and selling x pastries.
b) Determine the break-even point for the bakery.
A) a. P(x) = 0.7x + 770; b. 1,100 pastries
B) a. P(x) = 1.60x - 770; b. 481 pastries
C) a. P(x) = 1.60x + 770; b. 481 pastries
D) a. P(x) = 0.7x - 770; b. 1,100 pastries

Question

Quizplus · Accepted Answer

The profit function, P(x), is found by subtracting the total costs from the total revenue. The total revenue from selling x pastries is $1.60x. The total cost includes the fixed cost of $770 and the variable cost of $0.90 per pastry, which is $0.90x. Therefore, the profit function is P(x) = 1.60x - (0.90x + 770) = 0.7x - 770. The break-even point occurs when P(x) = 0, so solving 0.7x - 770 = 0 gives x = 1,100 pastries.

Solve the Problem. -A Bakery Makes and Sells Pastries. the Fixed Monthly Cost