Answer with Explanation:
1. Marginal Cost per Unit
As we know:
Marginal Cost per Unit = Change in Cost / Change in Quantity Bought
= ($3580 - $2280) / (500 - 100)
= $3.25 per Unit
2. Fixed Cost to setup
The fixed cost would be $2280 because it is the cost that is required for setting up the kiosk. The cost $3580 is not relevant because it depends on the demand of the product. The least cost to set up kiosk is $2280.
3. Cost Function
Total Cost = Fixed Cost + Variable Cost
As we know that:
Variable Cost = Marginal cost per unit * Number of units = $3.25 * x = 3.25x
For Fixed cost $2280
By putting this value in the above equation, we have:
Total Cost = $2280 + 3.25x
C(x) = $2280 + 3.25x
And
For Fixed cost $3580
C(x) = $3580 + 3.25x
4. Revenue Function
Total Revenue = Selling Price per Unit * Total Units
Here
Selling price is $8 and total units are "x"
By putting values, we have:
Total Revenue = $8 * x
R(x) = 8x
5. Breakeven Point For $2280 and $3580
As we know that
Breakeven Point = Fixed Cost / Contribution Per unit
For Fixed Cost $2280:
Breakeven Point = $2280 / ($8 - $3.25)
= 480 Units
For Fixed Cost $2280:
Breakeven Point = $3580 / ($8 - $3.25)
= 754 Units
6. Profit Function
For Fixed Cost $2280:
Profit = Revenue Function - Cost Function
P(x) = 8x - ($2280 + 3.25x)
P(x) = 8x - $2280 - 3.25x
P(x) = 4.75x - $2280
For Fixed Cost $3580:
P(x) = 4.75x - $3580
7. Claire's Profit if she sells 1,000 bottles
Using the above profit function for fixed cost $2280, we have:
P(x) = 4.75x - $2280
Here x is 1,000 units, which means:
P(x) = 4.75 * 1,000 - $2280
P(x) = $4,750 - $2280 = $2,470
Using the above profit function for fixed cost $3,580, we have:
P(x) = 4.75x - $3,580
Here x is 1,000 units, which means:
P(x) = 4.75 * 1,000 - $3,580
P(x) = $4,750 - $3,580 = $1,170
