SOLUTION: A coffee company currently charges $2.40 per bag and sells 4,000 bags per week. The company plans to decrease the price per bag. Past experience indicates that each $0.10 price d
Question 1140520: A coffee company currently charges $2.40 per bag and sells 4,000 bags per week. The company plans to decrease the price per bag. Past experience indicates that each $0.10 price decrease raises weekly sales by 400 bags.How much should be charged per bag in order to attain the maximum revenue Answer by greenestamps(13200) (Show Source):
Suppose the company decreases the price by $0.10 x times from the current cost of $2.40; the number of bags sold will increase by 400 x times from the current 4000.
Then the cost per bag will be $2.40 minus $0.10 x times; the number of bags sold will be 4000 plus 400 x times.
The total revenue is then
Use any of a number of methods to find the maximum revenue.
Inspection shows the expression for total revenue will be a quadratic with a negative leading coefficient, so there will be a maximum value.
Use algebraic methods for finding the maximum value of a quadratic function;
or use calculus;
or graph the revenue function on a graphing calculator....
