Question

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

Answer 1

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

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Answer 2

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:

• $\mathbf{\dfrac{dN}{dx} = \dfrac{d}{dx}\Big( 1100 + 210 -5x^2 \Big)}$
• $\mathbf{\dfrac{dN}{dx}= 210 - 10x }$

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:

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