at a unit price of $900, the quantity demanded of a certain commodity is 75 pounds. if the unit price increases to $956, the quantity demanded decreases by 14 pounds. find the demand equation (assuming it is linear) where p is the unit price and x is the quantity demanded for this commodity in pounds.
p =
at what price are no consumers willing to buy this commodity? $
according to the above model, how many pounds of this commodity would consumers take if it was free?

a) 56x = 16800 - 14p  

b) $1200

c) 300 pounds

Step-by-step explanation:

Given:

At p₁ = $900 ; x₁ = 75 pounds

at p₂ = $956 ; x₂ = 75 - 14 = 61 pounds

Now,

from the standard equation of line, we have

on substituting the respective values, we get

or

( x - 75 ) × 56 = -14p + 12600

or

56x - 4200 = -14p + 12600

or

56x = 16800 - 14p        (relation between the unit price p and demand x)

b) For no consumers x = 0

thus, substituting in the relation we get

56 × 0 = 16800 - 14p

or

14p = 16800

or

p = $1200

c) For free , p = $0

on substituting in the above relation derived, we get

56x = 16800 - ( 14 × 0 )

or

x = 300 pounds

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a