This question is based on a standard modeling problem in business. The unit cost of a item (or drink or chemical) affects how much of the thing is sold. The revenue is the amount of money raised from sales. Hence, raising price should drop sales, but that may result in more revenue or less depending on whether the increased price per sale
Assume that a salesman predicts the sales for a particular liquid to be S = 750 – 42p , where p is the price per gallon set by the company. Suppose the company wants to sell at least 300 gallons in a month. To the nearest cent, what should the price be?
To find the price that the company should set in order to sell at least 300 gallons in a month, we can use the information given in the salesman's prediction equation.
The prediction equation is given as S = 750 - 42p, where S represents the predicted sales and p represents the price per gallon.
Since the company wants to sell at least 300 gallons in a month, we can set up an inequality as follows:
S ≥ 300
Substituting the prediction equation into the inequality, we get:
750 - 42p ≥ 300
To solve this inequality, we can start by isolating the variable p by subtracting 750 from both sides:
-42p ≥ 300 - 750
Simplifying further:
-42p ≥ -450
Next, divide both sides of the inequality by -42. But remember that whenever we divide or multiply an inequality by a negative number, the inequality sign must be reversed:
p ≤ (-450) / (-42)
Simplifying:
p ≤ 10.714
To the nearest cent, the price p should be set at $10.71 in order to sell at least 300 gallons in a month.