Final answer:
To find the number of regular-price guests and discount guests at the breakeven point in the Bijou Museum, we need to consider the revenue and costs associated with each group. Revenue from regular-price guests is $10.5x, revenue from discount guests is $2.5x, and the total revenue is $13x. The equation that represents the breakeven point is 11x - 2y = 66,000.
Step-by-step explanation:
To find the number of regular-price guests and discount guests at the breakeven point in the Bijou Museum, we need to consider the revenue and costs associated with each group. Let's denote the number of regular-price guests as x, and the number of discount guests as y.
Revenue from regular-price guests = 0.75 * x * $14 = $10.5x
Revenue from discount guests = 0.25 * x * $10 = $2.5x
Total revenue = $10.5x + $2.5x = $13x
Variable cost per guest is $2 for both groups, so the total variable cost is 2*(x+y).
Fixed costs are $66,000 per month.
At the breakeven point, the total revenue equals the total costs. Therefore, $13x = 2*(x+y) + $66,000.
Simplifying the equation, we get 11x - 2y = 66,000.
Since we have one equation with two variables, we cannot determine the exact values of x and y. However, we can use trial and error to find possible values that satisfy the equation and represent the number of regular-price guests and discount guests at the breakeven point.