Answer:
a. The price that should be charged if the demand is 40 million gallons is $20.25.
b. The demand decreases by 16 millions of gallons.
Step-by-step explanation:
We know that the price-demand equation for gasoline is given by
[tex]0.1 x + 4 p = 85[/tex]
where
p is the price per gallon in dollars and
x is the daily demand measured in millions of gallons.
a. To find what price should be charged if the demand is 40 million gallons you must
Solve for p,
[tex]0.1x\cdot \:10+4p\cdot \:10=85\cdot \:10\\x+40p=850\\40p=850-x\\p=\frac{850-x}{40}[/tex]
We know that the demand is 40 million gallons (x = 40). So,
[tex]p=\frac{850-40}{40}=\frac{81}{4}=20.25[/tex]
b. To find how much does the demand decrease when the price increases by $0.4 you must
Solve for x,
[tex]0.1x\cdot \:10+4p\cdot \:10=85\cdot \:10\\x+40p=850\\x=850-40p[/tex]
We know that the price increases by $0.4. So,
[tex]-40\left(0.4\right)=-16[/tex]
The demand decreases by 16 millions of gallons.
