Answer:
Part A)
For 10 boxes [tex]P=-\$2,479.10[/tex]
For 40 boxes [tex]P=-\$1,951.40[/tex]
For 25 boxes [tex]P=-\$2,215.25[/tex]
Part B) The number of boxes must be greater than or equal to 191 for a profit of at least $700
Part C) 151 boxes are needed to break even
Step-by-step explanation:
we know that
Profit, is equals to revenue minus costs of goods sold
we have
[tex]P=17.59x-2,655[/tex]
Part A) Find the profit for
1) 10 boxes
For x=10 boxes
substitute in the formula
[tex]P=17.59(10)-2,655[/tex]
[tex]P=-\$2,479.10[/tex]
The negative means that the revenue is less than the costs
2) 40 boxes
For x=40 boxes
substitute in the formula
[tex]P=17.59(40)-2,655[/tex]
[tex]P=-\$1,951.40[/tex]
The negative means that the revenue is less than the costs
3) 40 boxes
For x=25 boxes
substitute in the formula
[tex]P=17.59(25)-2,655[/tex]
[tex]P=-\$2,215.25[/tex]
The negative means that the revenue is less than the costs
Part B) How many boxes needed for a profit of at least $700?
For P=$700
substitute in the formula and solve for x
[tex]700=17.59x-2,655[/tex]
[tex]17.59x=2,655+700[/tex]
[tex]17.59x=3,355[/tex]
[tex]x=190.7\ boxes[/tex]
Round up
[tex]x=191\ boxes[/tex]
therefore
The number of boxes must be greater than or equal to 191 for a profit of at least $700
Part C) How many boxes needed to “break even”?
we know that
Break even is when the profit is equal to zero
For P=0
[tex]0=17.59x-2,655[/tex]
[tex]17.59x=2,655[/tex]
[tex]x=150.9[/tex]
Round up
151 boxes are needed to break even
