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An oil-producing country can sell 7 million barrels of oil a day at a price of $80 per barrel. If each $1 price increase will result in a sales decrease of 100,000 barrels per day, what price will maximize the country's revenue?

$

How many barrels will it sell at that price?
barrels

User Howli
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1 Answer

2 votes

Answer:

Explanation:

To find the price that maximizes the country's revenue, we need to consider the relationship between price, sales, and revenue.

Let's start by calculating the current revenue for the country:

Revenue = Price × Sales

Revenue = $80/barrel × 7 million barrels/day

Revenue = $560 million/day

Now let's consider the effect of a price increase on sales. According to the problem, a $1 increase in price will result in a decrease of 100,000 barrels/day in sales. This means that the new sales rate at a price of $81/barrel will be:

New sales = 7 million barrels/day - 100,000 barrels/day per $1 increase × (81 - 80)

New sales = 6.9 million barrels/day

The new revenue at a price of $81/barrel will be:

New revenue = $81/barrel × 6.9 million barrels/day

New revenue = $559.9 million/day

We can repeat this process for a range of prices to see how revenue changes:

Price Sales (million barrels/day) Revenue (million $/day)

80 7.0 560.0

81 6.9 559.9

82 6.8 544.0

83 6.7 534.1

84 6.6 528.0

85 6.5 520.0

From this table, we can see that the price that maximizes revenue is $84/barrel. At this price, the country will sell 6.6 million barrels/day, and generate revenue of $528 million/day.

Therefore, the price that will maximize the country's revenue is $84/barrel, and it will sell 6.6 million barrels/day at that price.

User James Heald
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