Question
In: Math
The manufacturer of a brand of mattresses will make x hundred units available in the market...
The manufacturer of a brand of mattresses will make x hundred units available in the market when the unit price is
p = 150 + 60e0.05x
dollars.
(a) Find the number of mattresses the manufacturer will make
available in the market place if the unit price is set at
$350/mattress. (Round your answer to the nearest integer.)
(b) Find the producers' surplus if the unit price is set at
$350/mattress. (Round your answer to the nearest dollar.)
$
Solutions
Expert Solution
Given that
where p is the unit price in dollars to supply x hundred units of mattresses in the market.
(a)
The unit price p is set at $350 per mattress.
The number of mattresses that will be supplied to the market is
Rounding to the nearest integer, we get
Hence, the number of mattresses the manufacturer will make available in the market place is 2408.
(b)
The producers' surplus at x = a is given by the formula
From part (a) we get when the unit price p is $350 per mattress, x = 24.08 hundred units
Hence, the producers' surplus at x = 24.08 is given by
Hence, the producers' surplus when the unit price is set at $350 per mattress is approximately 2016 dollars(rounding to the nearest dollar).
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