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Anastaziya [24]
3 years ago
11

You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for

its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers has the linear form q = mp + b, where p is the price per hamburger, q is the demand in weekly sales, and m and b are certain constants you must determine.
Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 9000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero.
(A) Use these data to find the linear demand function q(p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week.
Mathematics
1 answer:
BartSMP [9]3 years ago
3 0

Answer:

The demabd function is:

q(p)= -4500p+18000

Step-by-step explanation:

The demand follow the linear equation q(p)=mp+b

1. When p=$2.00 and q=9000, the equation is:

9000=m(2.00)+b     (1)

2. Whe p=$4.00 and q=0, the equation is:

0=m(4.00)+b  (2)

3. Solve equation (1) for b:

9000=2m+b\\9000-2m=2m+2m+b\\9000-2m=b

4. Replace the value of b in equation (2)

0=4m+b\\0=4m+9000-2m\\0=2m+9000\\0-9000=2m+9000-9000\\-9000=2m\\\frac{-9000}{2m}=\frac{2m}{2m}\\ -4500=m

The value of m is 4500

5. Calculate b, replacing m:

0=4m+b\\\\0=4(-4500)+b\\0=-18000+b\\18000=b

The value of b is 18000

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Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

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Part (c)

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Part (d)

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We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

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