Question

Carolina makes wind chimes to sell at the local street market. As Carolina produces a greater number of wind chimes, she can lower the price per unit. The function v(x) = 48 - 22x relates the price v to the number produced. The cost of making x wind chimes can be represented with the function c(x) = 12x + 64.

a. How many wind chimes should Carolina sell each week to maximize her profit?

2
3
4
5
Carolina's best business plan is to produce and sell 4 wind chimes per week, for a weekly profit of $96.

Answer 1

Doggies Paradise Inc. should produce and sell five dog coats to maximize its profit based on the calculations of total revenue, marginal revenue, total cost, and marginal cost for each output level. The profit-maximizing quantity is the level at which marginal revenue equals marginal cost, which is five units in this case.

Step-by-step explanation:

Total Revenue and Total Cost:-

In order to calculate total revenue, we multiply the price of the dog coats ($72) by the quantity sold. For example, at a quantity of 1, the total revenue is $72. At a quantity of 2, the total revenue is $144. The table below shows the total revenue for each output level from one to five units:

* Quantity 1: Total Revenue = $72
* Quantity 2: Total Revenue = $144
* Quantity 3: Total Revenue = $216
* Quantity 4: Total Revenue = $288
* Quantity 5: Total Revenue = $360

We can see that the total revenue increases as the quantity sold increases.

Marginal Revenue and Marginal Cost:-

Marginal revenue is the additional revenue earned from selling one additional unit. For example, at a quantity of 2, the marginal revenue is $72. At a quantity of 3, the marginal revenue is $72. The table below shows the marginal revenue for each output level from one to five units:

* Quantity 1: Marginal Revenue = $72
* Quantity 2: Marginal Revenue = $72
* Quantity 3: Marginal Revenue = $72
* Quantity 4: Marginal Revenue = $72
* Quantity 5: Marginal Revenue = $72

Marginal cost is the additional cost incurred from producing one additional unit. The table below shows the marginal cost for each output level from one to five units:

* Quantity 1: Marginal Cost = $64
* Quantity 2: Marginal Cost = $20
* Quantity 3: Marginal Cost = $30
* Quantity 4: Marginal Cost = $70
* Quantity 5: Marginal Cost = $86

We can see that the marginal cost increases as the quantity produced increases.