SOLUTION: The demand function for an office supply company's line of plasic rulers is p= 0.45- 0.00045q, where p is the price (in dollars) per unit when q units are demanded(per day) by cons
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Question 187637This question is from textbook mathematical analysis
: The demand function for an office supply company's line of plasic rulers is p= 0.45- 0.00045q, where p is the price (in dollars) per unit when q units are demanded(per day) by consumers. Find the level of production that will minimize the mufacture's total revenue, and determine this revenue.
Please with full details, thanks This question is from textbook mathematical analysis
You can put this solution on YOUR website! The demand function for an office supply company's line of plastic rulers is
p = 0.45 - 0.00045q, where p is the price (in dollars) per unit when q units
are demanded(per day) by consumers.
I think it should be:
Find the level of production that will maximize the manufacturer's total
revenue, and determine this revenue.
:
p = 0.45 - 0.00045q
:
Level of production = q
:
Revenue = quantity * price
r = q * p
;
Replace p with (.45-.00045q) in the above equation and you have
r = q * (.45-.00045q)
r = .45q - .00045q^2
Arrange as a quadratic equation:
r = -.00045q^2 + .45q
:
We can find the value of q which gives max amt by using the eq: x = -b/(2a)
in this equation that would be
q =
q =
q = +500 units need to be produced for max revenue
:
Then it says,"and determine this revenue"
Substitute 500 for q in the revenue equation (r = -.00045q^2 + .45q)
r = -.00045(500^2) + .45(500)
r = -.00045(250000) + 225
r = -112.5 + 225
r = $112.5 is the max revenue and occurs when you produce 500 units
:
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