Question

Pattle's Produce charges $2.29 for a package of strawberries. On average, Pattle's Produce sells 95 packages of strawberrles dally. They estlmate that for each 20-cent Increase In the cost of a package of strawberrles, 9 less packages wll be sold each day. Let x represent the number of 20-cent Increases In the cost of a package of strawberrles. Whlch Inequality represents the values of x that would allow Pattle's Produce to have a dally revenue of at least $255 from selling the packages of strawberrles?

A.-1.872 + 21.61r + 217.55255
B.-1.872 + 1.61r +217.55 255
C. -1.82- 21.61r + 217.55255
D.-1.872- 1.61r + 217.55 255.​

Answer 1

The correct inequality to represent the values of x that would allow Pattle's Produce to have a daily revenue of at least $255 from selling packages of strawberries is option C: -1.8x^2 - 21.5x + 217.55 ≥ 255.

Step-by-step explanation:

To determine which inequality represents the values of x that would allow Pattle's Produce to have a daily revenue of at least $255 from selling packages of strawberries, we first need to establish an equation for their daily revenue. Let's do that step by step.

The initial price is $2.29 and the initial daily sales are 95 packages. For each 20-cent increase, there is a decrease of 9 packages in daily sales. We are looking for an inequality that ensures daily revenue is at least $255.

The equation for revenue after x increases of $0.20 in the price and x decreases of 9 packages in daily sales is:

Revenue = (Initial Price + $0.20x) × (Initial Sales - 9x)

Putting the values in, we get: Revenue = ($2.29 + $0.20x) × (95 - 9x)

For a daily revenue of at least $255, the inequality would be:

($2.29 + $0.20x) × (95 - 9x) ≥ $255

Expanding and setting up the inequality gives us:

-1.8x^2 + 21.5x + 217.55 ≥ 255

Thus, the correct inequality is option C: -1.8x^2 - 21.5x + 217.55 ≥ 255.