Question

A rose garden can be planted for $4000. The marginal cost of growing a rose is estimated to $0.30,

Answer 1

Answer:

$C(x)=4000+0.3x$

$R(x)=1.75x$

$Profit= 1.45x-4000$

Step-by-step explanation:

We are given that A rose garden can be planted for $4000.

The marginal cost of growing a rose is estimated to $0.30,

Let x be the number of roses

So, Marginal cost of growing x roses = $0.3x$

Total cost = $4000+0.3x$

So, Cost function : $C(x)=4000+0.3x$ ---A

Now we are given that the total revenue from selling 500 roses is estimated to $875

So, Marginal revenue = $\frac{\text{Total revenue}}{\text{No. of roses}}$

Marginal revenue = $\frac{875}{500}$

Marginal revenue = $1.75$

Marginal revenue for x roses  = $1.75x$

So, Revenue function =  $R(x)=1.75x$ ----B

Profit = Revenue - Cost

$Profit= 1.75x-4000-0.3x$

$Profit= 1.45x-4000$  ---C

Now Plot A , B and C on Graph

$C(x)=4000+0.3x$  -- Green

$R(x)=1.75x$  -- Purple

$Profit= 1.45x-4000$  --- Black

Refer the attached graph