task: fixing the furnace\nivans furnace has quit working during the coldest part of the year, and he is…

task: fixing the furnace\nivans furnace has quit working during the coldest part of the year, and he is eager to get it fixed. he decides to call some mechanics and furnace specialists to see what it might cost him to have the furnace fixed. since he is unsure of the parts he needs, he decides to compare the costs based only on service fees and labor costs. shown below are the price estimates for labor that were given to him by three different companies. each company has given the same time estimate for fixing the furnace. y = 15x\n company a charges $35 per hour to its customers.\n company b charges a $20 service fee for coming out to the house and then $25 per hour for each additional hour.\n company c charges a $45 service fee for coming out to the house and then $20 per hour for each additional hour.\nif ivan thought the job should take one and one - half hours should ivan choose company a, company b, company c?\nif the job took three hours should ivan choose company a, company b, company c?\nif the job took six hours should ivan choose company a, company b, company c?\nsupport your decision with sound reasoning and representations. consider including equations, tables, and graphs.

task: fixing the furnace\nivans furnace has quit working during the coldest part of the year, and he is eager to get it fixed. he decides to call some mechanics and furnace specialists to see what it might cost him to have the furnace fixed. since he is unsure of the parts he needs, he decides to compare the costs based only on service fees and labor costs. shown below are the price estimates for labor that were given to him by three different companies. each company has given the same time estimate for fixing the furnace. y = 15x\n company a charges $35 per hour to its customers.\n company b charges a $20 service fee for coming out to the house and then $25 per hour for each additional hour.\n company c charges a $45 service fee for coming out to the house and then $20 per hour for each additional hour.\nif ivan thought the job should take one and one - half hours should ivan choose company a, company b, company c?\nif the job took three hours should ivan choose company a, company b, company c?\nif the job took six hours should ivan choose company a, company b, company c?\nsupport your decision with sound reasoning and representations. consider including equations, tables, and graphs.

Answer

Explanation:

Step1: Define cost - functions for each company

Let $x$ be the number of hours of labor. For Company A: The cost function $C_A(x)=35x$. For Company B: The cost function $C_B(x)=20 + 25x$ (a $20$ service - fee plus $25$ per hour). For Company C: The cost function $C_C(x)=45+20x$ (a $45$ service - fee plus $20$ per hour).

Step2: Calculate costs for $x = 1.5$ hours

For Company A: $C_A(1.5)=35\times1.5 = 52.5$. For Company B: $C_B(1.5)=20+25\times1.5=20 + 37.5=57.5$. For Company C: $C_C(1.5)=45+20\times1.5=45 + 30 = 75$. Since $52.5<57.5<75$, Ivan should choose Company A.

Step3: Calculate costs for $x = 3$ hours

For Company A: $C_A(3)=35\times3=105$. For Company B: $C_B(3)=20 + 25\times3=20+75 = 95$. For Company C: $C_C(3)=45+20\times3=45 + 60 = 105$. Since $95<105 = 105$, Ivan should choose Company B.

Step4: Calculate costs for $x = 6$ hours

For Company A: $C_A(6)=35\times6=210$. For Company B: $C_B(6)=20+25\times6=20 + 150=170$. For Company C: $C_C(6)=45+20\times6=45+120 = 165$. Since $165<170<210$, Ivan should choose Company C.

Answer:

If the job takes 1.5 hours, choose Company A. If the job takes 3 hours, choose Company B. If the job takes 6 hours, choose Company C.