MATH SOLVE

5 months ago

Q:
# 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 forthe Cost (5pts), Revenue (5pts) and Profit (5pts) functions and graph them all in the samecoordinate axes (30 pts). What is the break-even quantity? (5pt

Accepted Solution

A:

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] ---ANow we are given that the total revenue from selling 500 roses is estimated to $875So, 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] ----BProfit = Revenue - Cost [tex]Profit= 1.75x-4000-0.3x[/tex][tex]Profit= 1.45x-4000[/tex] ---CNow 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] --- BlackRefer the attached graph