A nut store sells 200 bags of almonds per month at a price of $5 per bag. For every $0.20 decrease in the price, the store sells five more bags per month. Determine the marginal revenue when 120 bags are sold.
To determine the marginal revenue when 120 bags are sold, we first need to find the price at which 120 bags are sold.
Let's assume that x represents the price decrease in dollars and y represents the increase in bags sold.
Given that for every $0.20 decrease in price, the store sells five more bags, we can write the equation for the relationship between x and y as:
y = (200 + 5x)
Now, let's find the value of x when 120 bags are sold:
120 = 200 + 5x
Subtracting 200 from both sides of the equation:
-80 = 5x
Dividing both sides of the equation by 5:
x = -16
Therefore, a price decrease of $16 will result in 120 bags sold.
Now, let's calculate the revenue for this price:
Revenue = (price per bag) * (number of bags sold)
Revenue = ($5 - $16) * 120 [Note: The price decrease is negative because it represents a decrease]
Simplifying the equation:
Revenue = $(-11) * 120
Revenue = -$1320
As you can see, with a price decrease of $16, the revenue becomes negative. This means that the marginal revenue when 120 bags are sold is -$1320.