Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can sell 300 plates but for each Ghc5 she raises the price,10 less plates are sold. A.Draw a table relating 5 different price levels with their corresponding number of plates sold.

B.Use the table to find the slope of the demand

C.Find the equation of the demand fraction.

D.Use your equation to determine the price in Ghc if she sells one plate of food to maximize her revenue

Sagot :

MrRoyal

The demand equation illustrates the price of an item and how it relates to the demand of the item.

  • The slope of the demand function is -1/2
  • The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]
  • The price that maximizes her revenue is: Ghc 85

From the question, we have:

[tex]Plates = 300[/tex]

[tex]Price = 20[/tex]

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{25-20}{290-300}[/tex]

[tex]m = \frac{5}{-10}[/tex]

[tex]m = -\frac{1}{2}[/tex]

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]

Open the brackets to calculate the maximum revenue

[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]

[tex]R(x) =6000 + 1300x - 50x^2[/tex]

Equate to 0

[tex]6000 + 1300x - 50x^2 =0[/tex]

Differentiate with respect to x

[tex]1300 - 100x =0[/tex]

Collect like terms

[tex]100x =1300[/tex]

Divide by 100

[tex]x =13[/tex]

So, the price at maximum revenue is:

[tex]Price= 20 + 5x[/tex]

[tex]Price= 20 + 5 * 13[/tex]

[tex]Price= 85[/tex]

In conclusion:

  • The slope of the demand function is -1/2
  • The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]
  • The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

https://brainly.com/question/21586143

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.