Answer:$641,200
Step-by-step explanation:
To find the company's expenses and revenue, we first need to calculate the quantity of shoes sold (q) at the given price (p = $69).
Given the demand function q = –200p + 30,000, we can substitute p = $69 into the equation:
q = –200(69) + 30,000
q = –13,800 + 30,000
q = 16,200
So, the company sells 16,200 pairs of shoes.
Now, let's calculate the expenses and revenue:
Expenses:
Manufacturing cost per shoe = $28
Fixed cost for the product line = $23,000
Total expenses = (Manufacturing cost per shoe * Quantity sold) + Fixed cost
= ($28 * 16,200) + $23,000
= $453,600 + $23,000
= $476,600
Revenue:
Price per shoe = $69
Quantity sold = 16,200
Total revenue = Price per shoe * Quantity sold
= $69 * 16,200
= $1,117,800
Profit:
Profit = Total revenue - Total expenses
= $1,117,800 - $476,600
= $641,200
So, the total profit earned at the end of the month is $641,200.
To calculate the total profit earned at the end of the month, we need to consider the following components:
Revenue: The total revenue earned by the company from the sales of the dancing shoes. The revenue function is given by:
Revenue
=
�
×
�
,
Revenue=p×q,
where
�
p is the price per shoe and
�
q is the demand function. Given the demand function
�
=
−
200
�
+
30
,
000
q=−200p+30,000, and the selling price of each shoe is $69, the revenue can be calculated as:
Revenue
=
69
×
(
−
200
×
69
+
30
,
000
)
.
Revenue=69×(−200×69+30,000).
Expenses: The total expenses consist of the fixed costs and the variable costs for manufacturing each shoe. The total variable costs are calculated as the cost to manufacture each shoe multiplied by the number of shoes produced, i.e.,
28
×
�
28×q. Hence, the total expense is:
Expense
=
23
,
000
+
28
×
�
.
Expense=23,000+28×q.
Profit: The profit can be determined by subtracting the expenses from the revenue:
Profit
=
Revenue
−
Expense
.
Profit=Revenue−Expense.
Let's start by calculating the value of
�
q when
�
=
69
p=69:
�
=
−
200
×
69
+
30
,
000
=
−
13
,
800
+
30
,
000
=
16
,
200.
q=−200×69+30,000=−13,800+30,000=16,200.
Thus,
�
=
16
,
200
q=16,200.
Next, we calculate the revenue:
Revenue
=
69
×
16
,
200
=
1
,
117
,
800.
Revenue=69×16,200=1,117,800.
Now, let's calculate the total expenses, given a fixed cost of $23,000 and variable costs of $28 per shoe:
Expense
=
23
,
000
+
(
28
×
16
,
200
)
=
23
,
000
+
453
,
600
=
476
,
600.
Expense=23,000+(28×16,200)=23,000+453,600=476,600.
Finally, the total profit can be calculated as:
Profit
=
1
,
117
,
800
−
476
,
600
=
641
,
200.
Profit=1,117,800−476,600=641,200.
Thus, the total profit earned by the company at the end of the month is $641,200.