Sunny Mountain Company will make 1970 snow blowers available when the unit price is $690. At a unit price of $780, they will market 5330 snow blowers.

Question

Sunny Mountain Company will make 1970 snow blowers available when the unit price is $690. At a unit price of $780, they will market 5330 snow blowers. Find the equation relating the unit price of a snow blower to the quantity supplied if the relationship is known to be linear.

 

p(x)=

 

How many snow blowers will be marketed when the unit price is $710? ( Round up to an integer)

 

What is the lowest price at which a snow blower will be marketed? (Round up to a whole dollar) $

Answer 1

p(x) is linear so it has the form p(x) = m*x + b and goes thru the points (1970,690) and (5330,780).  Find the slope 

 

m = (y₂ - y₁)/(x₂ - x₁) = (780 - 690)/(5330 - 1970) = 90/3360 = 3/112 

 

Use the first point (1970,690) and the slope 3/112 to find b 

 

690 = (3/112)*1970 + b

690 = 2955/56 + b

b = 690 - 2955/56 ~ 690 - 52.768 = 637.232

 

So p(x) = (3/112)*x + 637.23 

 

When p = $710 then 

 

710 = (3/112)*x + 637.23

(3/112)*x = 72.77

x = 72.77*(112/3) = 2716.75 ~ 2717 rounded up 

 

The lowest price is found when x = 1  

 

p(1) = (3/112)*1 + 637.23 = 637.26 = $638 rounded up