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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 s

ella [17]

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: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

From the question, we have:

$Plates = 300$

$Price = 20$

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

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

The slope (m) is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{25-20}{290-300}$

$m = \frac{5}{-10}$

$m = -\frac{1}{2}$

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:

$R(x) = (300 - 10x) \times (20 + 5x)$

Open the brackets to calculate the maximum revenue

$R(x) =6000 + 1500x - 200x - 50x^2$

$R(x) =6000 + 1300x - 50x^2$

Equate to 0

$6000 + 1300x - 50x^2 =0$

Differentiate with respect to x

$1300 - 100x =0$

Collect like terms

$100x =1300$

Divide by 100

$x =13$

So, the price at maximum revenue is:

$Price= 20 + 5x$

$Price= 20 + 5 * 13$

$Price= 85$

In conclusion:

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

Read more about demand equations at:

brainly.com/question/21586143

3 0

3 years ago

Calculate simple interest :

Elodia [21]

Answer:

the simple interest in both cases is 200 and 756 respectively

Step-by-step explanation:

The computation of the simple interest is shown below:

As we know that

Simple interest = P × r% × t

So

a. Simple interest is

= 2,500 × 8% × 1

= 200

b. The simple interest is

= 4,200 × 6% × 3

= 756

Hence, the simple interest in both cases is 200 and 756 respectively

5 0

3 years ago

What is the definition of a infinitely many solution equation

masya89 [10]

Answer:

Normally infinity means something that never ends, something that has no end, it goes on forever.

Step-by-step explanation:

I don’t actually know if this is right, but in math infinitely means something that goes on forever.

4 0

3 years ago

Read 2 more answers

Find the inverse of the function f f (x ) equals 9 x + 7

MrMuchimi

Note: Your question seems a little bit ambiguous. So, I am assuming the given function f(x)=9x+7.

Thus, I am solving based on it. It would still clear your concept.

Answer:

The inverse of f(x)=9x+7

$\frac{x-7}{9}$

Step-by-step explanation:

Given the function

$f(x)=9 x + 7$

A function g is the inverse of function f if for y=f(x), x=g(y)

Replace x with y

$x=9y+7$

solve for y

$9y=x-7$

$y=\:\frac{x-7}{9}$

Therefore,

The inverse of f(x)=9x+7 is:

$\frac{x-7}{9}$

i.e.

$\mathrm{Inverse\:of}\:9x+7:\quad \frac{x-7}{9}$

6 0

3 years ago

Does anyone know an equation for this table:

polet [3.4K]

Answer:

Don't know the exact equation but trying to explain

X is what the stuff that problem saying. Let's say you have books from library and you're returning them late you will pay $30 dollars for each of them

6 0

3 years ago