Suppose that Neptune Music has the copyright to the latest CD of the heavy Iron Band. The market demand schedule for the CD is:

Q = 800 – 100P.
Q represents quantity demanded measured in thousands of CDs and P represents the price in dollars. Production requires a fixed cost of $100,000 and a constant marginal cost of $2 per CD produced.

1.What price will maximize profits?
2.At the price you found in 1 above, how many CDs will be sold?
3.What is the maximum profit for the quantity and price you found above? level be in this case?

Here the function is demand Q=800-200P
Therefore,TR=PQ=800P-200P^2
MR=d(PQ)=800-2*200*P=800-400P
Here MC=2
Hence 800-400P=2
or -400P=-800+2=-798
or P=798/400=1.998
Again,Q=800-200P=800-200*1.995=389
Here Total cost(TC)=1000000+2*Q
Total Profit=TR-TC

Here the function is demand Q=800-200P
Therefore,TR=PQ=800P-200P^2
MR=d(PQ)=800-2*200*P=800-400P
Here MC=2
Hence 800-400P=2
or -400P=-800+2=-798
or P=798/400=1.998
Again,Q=800-200P=800-200*1.995=389
Here Total cost(TC)=1000000+2*Q(Most probably there is some mistake in the figure of total fixed cost)
Total Profit=TR-TC

The price that will maximize profits is $6.

At a price of $6, the quantity demanded will be 400,000 CDs.

The maximum profit will be $2,400,000, which is obtained by selling 400,000 CDs at a price of $6 each and incurring a fixed cost of $100,000 and a marginal cost of $800,000 (400,000 CDs x $2 per CD).

Ah, I see there's a little mistake in the calculation. No worries, Clown Bot is here to help!

1. To maximize profits, we need to find the price where marginal revenue (MR) equals marginal cost (MC). In this case, MR is 800 - 400P (derived from the demand function) and MC is 2. Plugging in MC = MR, we get 800 - 400P = 2. Solving for P gives P = (800 - 2) / 400 = 1.995 dollars.

2. To find the number of CDs sold at this price, we can plug P = 1.995 into the demand function: Q = 800 - 100P. Q = 800 - 100 * 1.995 = 600.5. Since we can't sell half of a CD, let's round it down to the nearest whole number. So, approximately 600 CDs will be sold.

3. Now, let's calculate the maximum profit. Total cost (TC) is the fixed cost of $100,000 plus the variable cost of $2 per CD multiplied by the quantity sold: TC = 100,000 + 2 * 600 = 100,000 + 1,200 = 101,200 dollars. Total revenue (TR) is the price of $1.995 multiplied by the quantity sold: TR = 1.995 * 600 = 1,197. Total profit is TR minus TC: Profit = TR - TC = 1197 - 101200 = -100,003.

Oh my, it seems like there's actually a loss of $100,003 at this quantity and price level. My apologies for the mistake, it looks like the pricing strategy needs some adjustment. Let's hope the Iron Band rocks harder on their next album!

1. To find the price that will maximize profits, we need to set marginal revenue (MR) equal to marginal cost (MC).

MR = 800 - 400P
MC = 2

Setting MR = MC, we have:
800 - 400P = 2

Solving for P, we get:
400P = 798
P = 798/400
P ≈ $1.995 (rounded to the nearest cent)

Therefore, the price that will maximize profits is approximately $1.995.

2. At the price of $1.995, we can substitute this value into the demand equation to find the quantity sold (Q).

Q = 800 - 200P
Q = 800 - 200(1.995)
Q ≈ 389

Therefore, approximately 389 thousand CDs will be sold.

3. To find the maximum profit, we need to calculate the total profit at the quantity and price found above.
Total Cost (TC) = Fixed Cost + (Marginal Cost * Quantity)

Fixed Cost = $100,000
Marginal Cost (MC) = $2
Quantity (Q) = 389

TC = $100,000 + ($2 * 389)
TC ≈ $100,000 + $778
TC ≈ $100,778

Total Revenue (TR) = Price * Quantity

TR = $1.995 * 389
TR ≈ $775.755

Total Profit = TR - TC
Total Profit ≈ $775.755 - $100,778
Total Profit ≈ -$100,002.245

The maximum profit for the quantity and price found above is approximately -$100,002.245. However, it is important to note that a negative profit indicates a loss, so in this case, Neptune Music would not be maximizing profits with the given demand and cost conditions.

To find the price that will maximize profits, we need to find the point where marginal revenue (MR) equals marginal cost (MC).

1. First, let's find the MR by taking the derivative of the total revenue (TR) function, which is PQ. In this case, TR = 800P - 200P^2. Taking the derivative, we get MR = 800 - 400P.

2. To find the price that maximizes profits, we set MR equal to MC. In this case, MC is a constant value of $2. So, we have the equation: 800 - 400P = 2.

3. Solving for P, we can subtract 800 from both sides of the equation: -400P = -798. Dividing both sides by -400, we get P = 1.995.

So, the price that will maximize profits is approximately $1.995 per CD.

To find how many CDs will be sold at this price, we can substitute this price into the demand equation given: Q = 800 - 100P. Substituting P = 1.995, we get Q = 800 - 100(1.995) = 789 CDs.

So, at the price of $1.995, approximately 789 CDs will be sold.

To find the maximum profit, we need to calculate the total cost (TC) and subtract it from the total revenue (TR).

Total cost (TC) = fixed cost + (marginal cost * quantity produced)
In this case, the fixed cost is $100,000 and the marginal cost is $2. Substituting the quantity produced (Q = 789) into the equation, we get TC = 100,000 + (2 * 789) = $101,578.

Total revenue (TR) = price * quantity sold
Substituting the price (P = 1.995) and quantity sold (Q = 789) into the equation, we get TR = 1.995 * 789 = $1,573.21.

Therefore, the maximum profit is calculated as follows:
Total profit = TR - TC = $1,573.21 - $101,578 = -$100,004.79.

It seems that there is a mistake in the figure of the total fixed cost, causing the total profit to be negative. Please double-check the figure provided for the total fixed cost to ensure accuracy.