(Solution) - Along distance telephone company is trying to determine the opti -(2025 Original AI-Free Solution)

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Along-distance telephone company is trying to determine the optimal pricing structure for its daytime and evening long-distance calling rates. It estimates the demand for phone lines as follows:

Daytime Lines (in 1000s) Demanded per Minute = 600 -5000Pd + 1000Pe
Evening Lines (in 1000s) Demanded per Minute = 400 + 3000Pd - 9500Pe

Where Pd represents the price per minute during the day and Pe represents the price per minute during the evening. Assume that it costs $100 per minute to provide every 1,000 lines in long-distance capacity. The company will have to maintain the maximum number of lines demanded throughout the day, even if the demand is greater during the day than during the evening.
a. What prices should the telephone company charge if it wants to maximize profit?
b. How many long-distance lines does the company need to maintain?