Simpsons, inc. can sell 500 pairs of boots per week if they charge $100 sales drop to 480 pairs per week if they charge $108. assume the price p is a linear function of the weekly demand for boots, q.
complete parts a-d below.

(a) complete the table:

demand, q price $
460
480 108
500 100
520
(b) write a formula for the demand function p = d(q)
type an expression using q as the variable.
(c) find the axis intercepts of d(q). interpret the intercepts by completing the following:
1. the quantity demanded is 0 boots when the price for a pair of boots is $
2. at a price of $0 (free), the demand is pairs of boots.
(d) interpret the slope of the line by completing the following:
1. lowering the price by s24 results in more pairs of boots sold per week.
2. raising the price by $ results in 70 fewer pairs sold per week.

  a) (demand, price) = (460, 116), (520, 92)

  b) p = 300 -0.4q

  c) $300; 750 pairs

  d) 60 pairs; $28

Step-by-step explanation:

a) For each change in demand by 20 pairs, the corresponding price change is $8 in the opposite direction. 460 pairs is 20 less than 480 pairs, so the corresponding price is $8 more than the $108 price for 480 pairs. That is, (q, p) = (460, $116).

Similarly, 520 is 20 more pairs than the 500 sold for $100, so the corresponding price is $8 less. That is, (q, p) = (520, $92).

__

b) The two-point form of the equation of a line will do.

  p = (p2 -p1)/(q2 -q1)(q -q1) +p1

  p = (100 -108)/(500 -480)(q -480) +108 . . . . substitute given table values

  p = -8/20(q -480) +108

  p = -0.4q +300 . . . . . . . simplify

__

c1) When q=0, p = -0.4·0 +300 = 300

  A price of $300 will bring demand to zero.

c2) When p=0, q can be found from 0 = -0.4q +300.

  q = 300/0.4 = 750

  When boots are free, 750 pairs will be demanded.

__

d1) The derivative of price with respect to quantity is the coefficient of q in the equation:

  dp/dq = -0.4

Then ...

  dq/dp = 1/(-0.4) = -2.5

For a change in price of -$24, the change in quantity sold will be ...

  Δq = (dq/dp)·Δp = (-2.5)(-24) = 60

  60 more pairs will be sold if the price is reduced by $24.

d2) As for the previous question, ...

  Δp = (dp/dq)·Δq = (-0.4)(-70) = 28

  Raising the price by $28 will result in 70 fewer pairs sold.

__

Using derivatives is a fancy way to say the relationship between change in price and change in quantity is ...

  Δq : Δp = 20 : -8 (given in the problem)

  = 60 : -24 (part d1 -- multiply by 3)

  = -70 : 28 (part d2 -- multiply by -3.5)

eveidence i thing that

step-by-step explanation:

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.