Question
b. Find the marginal cost, marginal revenue, and marginal profit when 70 parkas
are produced and sold using the formulas
,
and
.
Marginal cost:
Marginal revenue:
Marginal profit:
c. Use derivatives to estimate the marginal cost, marginal revenue, and marginal
profit when 70 parkas are produced and sold.
Marginal cost:
Marginal revenue:
are produced and sold using the formulas
and
Marginal cost:
Marginal revenue:
Marginal profit:
c. Use derivatives to estimate the marginal cost, marginal revenue, and marginal
profit when 70 parkas are produced and sold.
Marginal cost:
Marginal revenue:
Ask by Collins Fernandez. in the United States
Nov 06,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
Marginal profit when 70 parkas are produced and sold is $-1.2. For marginal cost and revenue using derivatives, we need the specific functions for cost and revenue.
Solution
To find the marginal profit when 70 parkas are produced and sold, we can use the formula for marginal profit:
Given:
- Marginal Cost = $0.8
- Marginal Revenue = $-0.4
Now, we can calculate the marginal profit:
So, the marginal profit when 70 parkas are produced and sold is:
Part c: Using Derivatives
To estimate the marginal cost, marginal revenue, and marginal profit using derivatives, we need the functions for cost
, revenue
, and profit
.
-
Marginal Cost: This is the derivative of the cost function
with respect to : -
Marginal Revenue: This is the derivative of the revenue function
with respect to : -
Marginal Profit: This is the derivative of the profit function
with respect to :
To provide numerical values for the marginal cost and marginal revenue using derivatives, we would need the specific functions
and
. If you have those functions, please provide them, and I can help you calculate the derivatives at
. If not, we can only state the formulas as shown above.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
When calculating the marginal profit, you can find it by subtracting the marginal cost from the marginal revenue. Using the provided values:
. Therefore, with a marginal cost of
and marginal revenue of
, the marginal profit would be
. So, the marginal profit is
.
To estimate the marginal cost, revenue, and profit using derivatives, recall that the derivative gives the rate of change at a point. If
represents the derivative of the cost function,
for revenue, and
for profit, you’d evaluate these derivatives at
. Assuming you’ve derived these functions prior to this, substituting
will yield the estimates for marginal cost and marginal revenue at that production level; however, you’ll need their specific expressions to perform the calculation.