MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

What is maximum weekly profit?

### Profit Model Use the models computed to find a model of the weekly profit using \( x \) as the independent variable. \[ P(x) = x^3 + x^2 - 42x + 96 \] **Note:** No calculator regression. Use the fact that profit revenue minus cost. The original form of the weekly profit model has roots at \( x = -5.26709, x = -1.74555, \) and \( x = 202.944 \), rounded to 3 decimal places. The adjusted form of the weekly profit model has roots at \( x = -8.9488 \) and \( x = 140.295 \), rounded to 3 decimal places. ### What is the maximum weekly profit? Round to the nearest dollar.
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Transcribed Image Text:### Profit Model Use the models computed to find a model of the weekly profit using \( x \) as the independent variable. \[ P(x) = x^3 + x^2 - 42x + 96 \] **Note:** No calculator regression. Use the fact that profit revenue minus cost. The original form of the weekly profit model has roots at \( x = -5.26709, x = -1.74555, \) and \( x = 202.944 \), rounded to 3 decimal places. The adjusted form of the weekly profit model has roots at \( x = -8.9488 \) and \( x = 140.295 \), rounded to 3 decimal places. ### What is the maximum weekly profit? Round to the nearest dollar.
**Vaster Outfitters manufactures and sells extreme-cold sleeping bags.** The table below shows the price-demand and total cost data, where: - \( p \) is the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags. - \( C \) is the total cost (in dollars) of producing \( x \) sleeping bags. | \( x \) (sleeping bags) | \( p \) | \( C \) | |------------------|-------|------| | 120 | 245 | 13,000 | | 150 | 220 | 15,000 | | 180 | 195 | 17,100 | | 200 | 155 | 18,500 | | 220 | 105 | 21,000 | --- ### Revenue Model Using the regression model computed above, find a model for the weekly revenue, using \( x \) as the independent variable. **NOTE:** Do not calculate another regression. Use the price equation to find a model for revenue. \[ R(x) = p \cdot x = (a + bx + cx^2)x = ax + bx^2 + cx^3 \] ### Cost Model Find a quadratic regression equation for the price-demand data, using \( x \) as the independent variable: \[ p = a + bx + cx^2 \] Round \( a \) to the nearest integer, round \( b \) to 2 decimal places, and round \( c \) to 4 decimal places. Find a linear regression model for the weekly cost data, using \( x \) as the independent variable. \[ C(x) = mx + k \] Round \( m \) to 1 decimal place, and round \( k \) to the nearest integer.
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Transcribed Image Text:**Vaster Outfitters manufactures and sells extreme-cold sleeping bags.** The table below shows the price-demand and total cost data, where: - \( p \) is the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags. - \( C \) is the total cost (in dollars) of producing \( x \) sleeping bags. | \( x \) (sleeping bags) | \( p \) | \( C \) | |------------------|-------|------| | 120 | 245 | 13,000 | | 150 | 220 | 15,000 | | 180 | 195 | 17,100 | | 200 | 155 | 18,500 | | 220 | 105 | 21,000 | --- ### Revenue Model Using the regression model computed above, find a model for the weekly revenue, using \( x \) as the independent variable. **NOTE:** Do not calculate another regression. Use the price equation to find a model for revenue. \[ R(x) = p \cdot x = (a + bx + cx^2)x = ax + bx^2 + cx^3 \] ### Cost Model Find a quadratic regression equation for the price-demand data, using \( x \) as the independent variable: \[ p = a + bx + cx^2 \] Round \( a \) to the nearest integer, round \( b \) to 2 decimal places, and round \( c \) to 4 decimal places. Find a linear regression model for the weekly cost data, using \( x \) as the independent variable. \[ C(x) = mx + k \] Round \( m \) to 1 decimal place, and round \( k \) to the nearest integer.
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