Question 993902: A manufacturer has 2900 units in stock. The product is now selling at $8 per unit. Next month the unit price will increase by $0.50. The manufacturer wants the total revenue received from the sale of the 2900 units to be no less than $23750. What is the number of units that can be sold this month?
At most _______ units
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if he sold all 2900 at 8 dollars each, he would get 23200 total.
that's 550 short of his goal of at least 23750.
the difference in price between 8 and 8.50 is .50.
take the 550 and divide it by .50 and you get 1100.
he would need to sell a minimum of 1100 units at 8.50.
2900 - 1100 = 1800.
he would therefore sell 1800 at 8.00 and 1100 at 8.50 and he would get 8 * 1800 = 14,400 + 8.50 * 1100 = 9,350 for a total orf 23,750.
you can also solve this algebraically as follows:
x = number of units sold at 8 dollars each.
y = number of units sold at 8.5 dollars each.
first equation is x + y = 2900
second equation is 8x + 8.5y >= 23750
from the first equation, solve for y to get y = 2900 - x
replace y with 2900 - x in the second equation to get:
8x + 8.5 * (2900-x) >= 23750
simplify to get:
8x + 24650 - 8.5x >= 23750
subtract 8x from both sides of this equation and subtract 23750 from both sides of this equation to get:
24650 - 23750 = 8.5x - 8x
simplify to get:
900 = .5x
divide both sides of this equation by 1.5 to get:
x = 1800.
since x + y = 2900, this means that y = 1100.
solution is x = 1800 and y = 1100
x is the number sold at 8 dollars
y is the number sold at 8.5 dollars
same answer as before when we used logic.
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