Answers:
16.50 for the first box
10 for the second box
======================================
Explanation:
Part (a)
Plug in x = 20 and solve for p.
0.2x+4p = 70
0.2*20+4p = 70
4 + 4p = 70
4p = 70-4
4p = 66
p = 66/4
p = 16.50
They should charge $16.50 per gallon if the demand is 20 million gallons.
------------------------
Part (b)
Let's say the price is initially $10 per gallon. The starting price could be anything you want.
Plug p = 10 into the equation and solve for x.
0.2x+4p = 70
0.2x+4*10 = 70
0.2x + 40 = 70
0.2x = 70-40
0.2x = 30
x = 30/(0.2)
x = 150
The demand is 150 million gallons if the price were $10 per gallon.
Now let's increase the price by $0.50 to get to p = 10.50
Let's solve for x based on this larger value of p.
0.2x+4p = 70
0.2x+4*10.50 = 70
0.2x+42 = 70
0.2x = 70-42
0.2x = 28
x = 28/(0.2)
x = 140
The demand is now 140 million gallons if the price were $10.50 per gallon.
The demand has gone down by 10 million gallons (since 150-140 = 10).
