Answer:
jia's friend should charge $22.33 for the dog washing sevice.
Explanation:
It is given that jia's friend provide fog washing service for each dog supplies cost $4 and wage are $5 .
A special room and equipment are needed ,at a cost of 400$ per month .
Fixed cost = $400
Variable cost = $4+$5=$9
Total cost of 30 dogs is
![C=400+9(30)=670](https://img.qammunity.org/2020/formulas/mathematics/middle-school/vrperyn490kx160joekny6t7mc2s4xdpkj.png)
Let x be the amount charged by jia's friend for the dog washing sevice. So, total revenue for 30 dogs washing service is
![R=30x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/iof00ef0fnrbocqq6189p8lpf78pjoekyt.png)
Formula for profit:
![Profit=Revenue-Cost](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hu49maixwtvryh3cvp9ktjlptjvy6uvbe3.png)
![Profit=30x-670](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ldfvr3h1n00rsfxxx8wfxobiywf5ws9rwh.png)
For break even condition, the profit is 0.
![0=30x-670](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yzjvobwmlgn05pvyy37z9sh0wxj1r0k4tp.png)
![-30x=-670](https://img.qammunity.org/2020/formulas/mathematics/middle-school/evx6k2r9sxsfpjhib9ck876k3yhgtlyic8.png)
![30x=670](https://img.qammunity.org/2020/formulas/mathematics/middle-school/syp5mi6o2yqlh4snl2y7o3nnnpgdu2no67.png)
Divide both sides by 30.
![(30x)/(30)=(670)/(30)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ftwhlwpormfc937en7200b4wujf9woy0yi.png)
![x=22.33](https://img.qammunity.org/2020/formulas/mathematics/middle-school/b3q5ah6264pzgv9ilqnahhxa2c3chqkyk1.png)
Therefore, jia's friend should charge $22.33 for the dog washing sevice.