The cost C (in dollars) of building a house is related to the number k of carpen

Question

The cost C (in dollars) of building a house is related to the number k of carpenters used and the number e of electricians used byt C(k, e) 15,000 50k2 + 60e2 If k e-20, compare the effects of increasing k by one unit and of increasing e by one unit. The effect of increasing k by one unit is to increase C by s The effect of increasing e by one unit is to increase C by $ Interpret the result. This means that, if you are currently using would cost you?to hire an additional carpenter ( carpenters and electricians to build a house, it ) than to hire an additional electrician ($

Explanation / Answer

C(k,e)=15000+50k^2+60e^2

If k=e=20 then cost to build the house= 15000+50×20×20+60×20×20=15000+20000+24000=59000

Cost to build the house when k=e=20 is $59000

Now if k increase by 1 means k= 20+1=21

Now cost = 15000+50×21×21+60×20×20= 15000+22050+24000=61050

So increase in C when k increase by 1 = 61050-59000=2050

Now if e increase by 1 then e=20+1=21

So cost to build the house when e=21 and k=20 is

15000+50×20×20+60×21×21=15000+20000+26460=61460

So increase in cost when e increase by 1=61460-59000=2460

So increase of cost when k increase by 1=$2050

And increase of cost when e increase by 1= $2460  

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