**Analyzing Demand and Cost Functions for Math Self-Help Videos***Understanding Demand and Cost for Profit Evaluation*To understand how changes in production levels affect profits, consider the given demand and cost functions for math self-help videos:- **Demand Function**: $ D(x) = 45 - 0.4x $- **Total Cost Function**: $ C(x) = 4x + 17 $*Task*: Evaluate the marginal profit function at $ x = 10 $.### Steps for Marginal Profit Evaluation:1. **Marginal Revenue (MR)**: \[ MR = \frac{d(D \cdot x)}{dx} \] Calculate the derivative of $ D(x) \cdot x $: \[ MR = \frac{d(45x - 0.4x^2)}{dx} = 45 - 0.8x \]2. **Marginal Cost (MC)**: \[ MC = \frac{dC}{dx} = \frac{d(4x + 17)}{dx} = 4 \]3. **Marginal Profit (MP)**: \[ MP = MR - MC = (45 - 0.8x) - 4 = 41 - 0.8x \]4. **Evaluate at $ x = 10 $**: \[ MP(10) = 41 - 0.8 \cdot 10 = 41 - 8 = 33 \]Therefore, the marginal profit at $ x = 10 $ is evaluated as 33.### Conclusion:- **Marginal Profit = 33**This implies:- **If production and sales increase by one unit, total profit will**: \[ \textcircled{ } \quad \text{increase} \quad \textcircled{ } \quad \text{decrease} \] - **By approximately**: \[ \text{33} \text{ dollars} \]

Demand Function for math self-help videos can be written as:P = 45 - 0.4x , where P is the price ,…

If the demand function for math self-help videos is given by 45 - 0.4x, and the total cost function to manufacture the videos is given by 4x + 17, evaluate the marginal profit function at x = 10. Marginal Profit = his means that if production and sales increase by one unit, then total profit will O increase O decrease y approximately dollars.

If the demand function for math self-help videos is given by 45 - 0.4x, and the total cost function to manufacture the videos is given by 4x + 17, evaluate the marginal profit function at x = 10. Marginal Profit = his means that if production and sales increase by one unit, then total profit will O increase O decrease y approximately dollars.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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