Sunny Mountain Company will make 1920 snow blowers available when the unit price is $660. At a unit price of $820, they will market 5260 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=  $660 + $0.0479/sb *(Q-1920 sb )

Explanation:

since the relationship between unit price and quantity is linear the following equation applies

P = P₁ + (P₂-P₁)/(Q₂-Q₁)*(Q-Q₁)

where P is the price for any quantity Q , while 1 and 2 represent the reference points. Thus

at P₁ =$660 → Q₁= 1920 snow blowers

at P₂=$820→ Q₂= 5260 snow blowers

we get

P = $660 + ($820-$660 )/(5260 -1920 )*(Q-1920) =  $660 + $0.0479/sb *(Q-1920 sb )

P=  $660 + $0.0479/sb *(Q-1920 sb )

Note:

- We can verify from the original equation that for Q=Q₁

P = P₁ + (P₂-P₁)/(Q₂-Q₁)*(Q₁-Q₁) =  P₁ + 0 = P₁

and for Q=Q₂

P = P₁ + (P₂-P₁)/(Q₂-Q₁)*(Q₂-Q₁) =  P₁ + P₂ -P₁  = P₂

thus the equation is correct