Final answer:
To maximize revenue for the chicken dinner, it should be set at a price of $50.
Step-by-step explanation:
To find the price at which the chicken dinner should be set to maximize revenue, we need to determine the value of x that maximizes the function R(x) = -0.5x(2x-100). We can do this by finding the critical points of the function.
To find the critical points, we can take the derivative of R(x) with respect to x, set it equal to zero, and solve for x. Then, we can test the values of x to determine if they correspond to a maximum or minimum.
By solving the derivative of R(x), we find two critical points: x = 0 and x = 50. To determine whether they correspond to a maximum or minimum, we can use the second derivative test or analyze the behavior of the function around those points. For R(x) = -0.5x(2x-100), we find that when x = 0, R(x) = 0, and when x = 50, R(x) = 1250. Therefore, the chicken dinner should be set at a price of $50 to maximize revenue.