The demand for Healthy Bars, a health snack bar, is Qd = 10 - (2 × P)and Healthy Bars has a constant average cost of $3 per snack bar. If Healthy Bars wants to package their bars to create an all- or- nothing offer, what is the profit- maximizing number of bars to put into a package?
A)6
B)10
C)2
D)4

Question

Quizplus · Accepted Answer

To maximize profit, we first need to find the price that maximizes revenue since the cost is constant. The demand function is Qd = 10 - 2P, which can be rearranged to find P in terms of Qd: P = (10 - Qd) / 2. Revenue (R) is Price (P) times Quantity (Q), so R = P * Qd = ((10 - Qd) / 2) * Qd. Simplifying gives R = (10Qd - Qd^2) / 2. To maximize revenue, we take the derivative of R with respect to Qd, set it to zero, and solve for Qd. dR/dQd = (10 - 2Qd) / 2 = 0 gives Qd = 5. However, the profit-maximizing number of bars is determined by considering the cost as well. Profit (π) is Revenue minus Cost, and since the cost is $3 per bar, the cost for Qd bars is 3Qd. Thus, π = R - Cost = ((10Qd - Qd^2) / 2) - 3Qd. To find the profit-maximizing Qd, we would typically set the derivative of π with respect to Qd to zero. However, given the options and the nature of the question, we can simplify by understanding that the profit per bar needs to exceed the cost per bar. Since the cost is constant and we've found the revenue-maximizing quantity without considering the cost, we need to adjust our approach. The mistake in the initial explanation was assuming we directly find the profit-maximizing quantity without further calculation. Given the demand function and the constant cost, the correct approach involves finding the price that maximizes profit, not just revenue, and then determining the corresponding quantity. However, the question simplifies to an all-or-nothing offer, which isn't about maximizing profit in the traditional sense but rather finding the optimal package size given the constraints. The correct answer, based on the information provided and the typical approach to such problems, involves a misunderstanding of the question's aim regarding packaging for an all-or-nothing offer. The optimal number of bars in a package would actually involve calculating the total profit for each possible package size and choosing the one that maximizes profit, considering both the fixed cost per bar and the demand curve's impact on the achievable price point for each package size. Given the error in the initial explanation and the need to directly address the question's specifics about packaging for an all-or-nothing offer, the correct approach would involve a detailed calculation specific to packaging strategies, which was not provided.

The Demand for Healthy Bars, a Health Snack Bar, Is