The demand function for a certain kind of mattress is given by p = 600e^−0.04x where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded each month. (a) Find the number of mattresses demanded per month if the unit price is set at $250 per mattress. (b) Use the results of part (a) to find the consumers’ surplus if the selling price is set at $250 per mattress.
2.The demand function for a certain kind of mattress is given by
p = 600e^−0.04x
where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded each month.
(a) Find the number of mattresses demanded per month if the unit price is
set at $250 per mattress.
(b) Use the results of part (a) to find the consumers’ surplus if the selling
price is set at $250 per mattress.
PART 2 of number 2: The manufacturer of the brand of mattress of problem #2 will make x hundred units available in the market when the unit price in dollars is p = 100 + 80e^0.05x
(a) Find the number of mattresses demanded per month of the unit price is
set at $400 per mattress.
(b) Use the results of part (a) to find the producers’ surplus if the selling price is set at $400 per mattress.
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