Suppose that a golf$-$course operator observers that the demand for tee times is different during the week than during the weekend.$$ The weekly demand curve for each market segment is summarized below.

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Segment $1$: Weekday Golfers

Demand Curve:$$ P$1=120-$Q$1$

Marginal Revenue: $$ MR$1=120-2$Q$1$

where $$ P$1=$ Segment $1($weekday golfer$)$ price

Q$1=$ Segment $1($weekday golfer$)$ quantity demanded per week

Segment $2$: Weekend Golfers

Demand Curve:$$ P$2=200-2$Q$2$

Marginal Revenue: $$ MR$2=200-4$Q$2$

where $$ P$2=$ Segment $2($weekend golfer$)$ price

Q$2=$ Segment $2($weekend golfer$)$ quantity demanded per week

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If the market was not segmented, the weekly demand curve for the overall market would be:

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Demand Curve:$$

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Marginal Revenue: $$

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where $$ P $=$ price paid, regardless of day of week

Q $=$ quantity demanded per week

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The total weekly cost of operating the golf course is TC $=1,500+4$Q$1+4$Q$2$

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$3.(8$ points$)$ Suppose the golf$-$course operator is able to segment the market, offering a separate weekday and weekend price. What is the optimal quantity of tee$-$times sold per week to Segment $1($weekday golfers$)?$ What is the optimal price that these customers should be charged?$$ What is the optimal quantity of tee$-$times sold per week to Segment $2($weekend golfers$)?$ What is the optimal price that these customers should be charged? What is golf$-$course operator$$s weekly profit across the two market segments?$$ Be sure to show your work, including all calculations and conditions used.

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$4.(4$ points$)$ Suppose the golf$-$course operator does not separate the market into segments, charging a single price to all customers regardless of day of week.$$ What is the optimal quantity of tee$-$times sold per week?$$ What is the optimal price in the overall $($or un$-$segmented$)$ market?$$ What is the golf$-$course operator$$s associated weekly profit?$$ Be sure to show your work, including all calculations and conditions used.