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fredd [130]
3 years ago
6

On Saturday Lindsay walked 3 1/2 mile in 1 and 2/5 hours what was her walking pace in miles per hour write in simplest form

Mathematics
1 answer:
Makovka662 [10]3 years ago
7 0

Answer:

If she walked 3.5 miles in 1.4 hours, then her pace was:

 3.5 miles / 1.4 hours = 2.5 miles/hour

Step-by-step explanation:

To get her pace in miles per hour, you take the number of miles and divide by the number of hours.  

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Answer:

a) Demand function: q=6000-10\cdot p

b) The rebate should be of $200, so the sale price becomes $300 per unit.

c) The rebate should be of $150, so the sale price becomes $350 per unit.

Step-by-step explanation:

a) In this case, we have a known point of the demand function (1000 units sold at $500), and the slope of a linear function (increase by 100 units fora decrease in $10).

We can express the demand function (linear) as:

q=b+m\cdot p

To calculate the slope m, we use:

m=\Delta q/\Delta p=(+100)/(-10)=-10

To calculate b, we use the known point and the calculated slope:

q=b+m\cdot p\\\\b=q-m\cdot p=1000-(-10)\cdot (500)=1000+5000=6000

Then the demand function is:

q=6000-10\cdot p

b) The revenue can be expressed as:

R=q\cdot p = (6000-10p)\cdot p=6000p-10p^2

To maximize, we can derive and equal to zero

dR/dp=6000-2*10p=0\\\\20p=6000\\\\p=300

The rebate should be of $200, so the sale price becomes $300 per unit.

c) If we take into account the cost, we have that

R=q\cdot p-C=(6000p-10p^2)-(68000+100q)\\\\R=(6000p-10p^2)-(68000+100(6000-10p))\\\\R=6000p-10p^2-(68000+600000-1000p)\\\\R=-10p^2+7000p-668000

To maximize, we can derive and equal to zero

dR/dp=-20p+7000=0\\\\p=7000/20=350

The rebate should be of $150, so the sale price becomes $350 per unit.

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