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

and the total revenue from selling 500 roses is estimated to $875. Write down the equations for

the Cost (5pts), Revenue (5pts) and Profit (5pts) functions and graph them all in the same

coordinate axes (30 pts). What is the break-even quantity? (5pt

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wifilethbridge wifilethbridge · Answer 1 · 2019-09-17T08:03:26+02:00

Answer:

[tex]C(x)=4000+0.3x[/tex]

[tex]R(x)=1.75x[/tex]

[tex]Profit= 1.45x-4000[/tex]

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 = [tex]0.3x[/tex]

Total cost = [tex]4000+0.3x[/tex]

So, Cost function : [tex]C(x)=4000+0.3x[/tex] ---A

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

So, Marginal revenue = [tex]\frac{\text{Total revenue}}{\text{No. of roses}}[/tex]

Marginal revenue = [tex]\frac{875}{500}[/tex]

Marginal revenue = [tex]1.75[/tex]

Marginal revenue for x roses = [tex]1.75x[/tex]

So, Revenue function = [tex]R(x)=1.75x[/tex] ----B

Profit = Revenue - Cost

[tex]Profit= 1.75x-4000-0.3x[/tex]

[tex]Profit= 1.45x-4000[/tex] ---C

Now Plot A , B and C on Graph

[tex]C(x)=4000+0.3x[/tex] -- Green

[tex]R(x)=1.75x[/tex] -- Purple

[tex]Profit= 1.45x-4000[/tex] --- Black

Refer the attached graph