After spending $x in advertising per day, a McDonalds restaurant finds that it sells N hamburgers where N = 1000 + 210x − 5x 2 . Estimate using differentials how many m

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02-11-2021
Mathematics

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After spending $x in advertising per day, a McDonalds restaurant finds that it sells N hamburgers where N = 1000 + 210x − 5x 2 . Estimate using differentials how many m

Sagot :

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Fichohidn Fichohidn · Answer 1 · 2021-11-10T08:57:29-05:00

Increasing the daily spending from $16 to $16.80 would mean that the number of burgers sold would will increase by 37.

N = 1000 + 210x - 5x²

N = number of burgers sold

x = daily spending

At x = $16.00

Number of burgers sold would be:

N = 1000 + 210(16) + 5(16²)

N = 1000 + 3360 - 1280

N = 3080 burgers

At x = $16.80 :

Number of burgers that would be sold :

N = 1000 + 210(16.80) + 5(16.80²)

N = 1000 + 3528 - 1411.2

N = 3116.8 burgers

Therefore, the Increase in the number of burgers sold :

(3116.8 - 3080) = 36.8 burgers

Learn more :https://brainly.com/question/25381260

Ajeigbeibraheemidn Ajeigbeibraheemidn · Answer 2 · 2021-11-10T09:12:30-05:00

The number of hamburgers the restaurant will sell if it increases its daily spending on advertising from $17 to $17.80 is 32 more hamburgers.

This question wants us to use the differential method to estimate the number of hamburgers the restaurant will sell if it increases its daily spending on advertising from $17 to $17.80.

Given that;

McDonalds sell N hamburgers where N = 1000 + 210x - 5x²

The differential for the above equation:

[tex]\mathbf{\dfrac{dN}{dx} = \dfrac{d}{dx}\Big( 1100 + 210 -5x^2 \Big)}[/tex]
[tex]\mathbf{\dfrac{dN}{dx}= 210 - 10x }[/tex]

Suppose x is increased by $Δx, we can then infer that the increase in ΔN in N can be computed as:

ΔN ≅ N'(x) × Δx
ΔN = (210 -10) × Δx

where;

Δx = 17.80 - 17.00
Δx = 0.8

∴

ΔN = (210 -10) × 0.80
ΔN = 40 × 0.8
ΔN = $32

Therefore, we can conclude that the number of hamburgers the restaurant will sell if it increases its daily spending on advertising from $17 to $17.80 is 32 more hamburgers.

Learn more about differential method here:

https://brainly.com/question/18252932?referrer=searchResults

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