Question 587732: Midtown Delivery Serive delivers packages which cost $1.50 per package to deliver. The fixed cost to run the delivery truck in $250.00 per day. If the company charges $4.00 per package, how many packages must be delivered daily to make a profit of $39.00?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of deliveries
revenue = 4x
cost = 250 + 1.5x
profit = revenue minus cost = 4x - 250 - 1.5x which becomes:
profit = 2.5x - 250
since profit is to be 39 dollars, then equation becomes:
39 = 2.5x - 250
add 250 to both sides of this equation to get:
289 = 2.5x
divide both sides of this equation by 2.5 to get:
x = 289/2.5
answer is x = 115.6
since 6/10ths of a package can't be delivered, then the answer is"
x = 116.
deliver 116 packages and profit is greater than 39.
deliver 115 packages and profit is less than 39.
116 * 4 = 464
115 * 4 = 460
that's revenue.
cost is:
116 * 1.5 + 250 = 424
115 * 1.5 + 250 = 422.5
profit equals revenue minus cost:
for x = 116:
profit = 464 - 424 = 40
for x = 115:
profit = 460 - 422.5 = 37.5
with 116 packages delivered, profit is greater than 39.
with 115 packages delivered, profit is less than 39.
when number of package delivered is 115.6, the profit is exactly 39, but this isn't possible.
still, for x = 115.6
revenue = 115.6 * 4 = 462.4
cost = 115.6 * 1.5 + 250 = 423.4
profit = revenue - cost = 462.4 - 423.4 = 39
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