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 by† C(k, e) = 15,000 + 50k2 + 60e2. If k = e = 15, 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 $ The effect of increasing e by one unit is to increase C by $ Interpret the result. This means that, if you are currently using carpenters and electricians to build a house, it would cost you to hire an additional carpenter ($ ) than to hire an additional electrician ($ ).

Explanation / Answer

C(k, e) = 15,000 + 50k^2 + 60e^2

With k = e = 15 :
C(15 , 15) = 15000 + 50(15)^2 + 60(15)^2
C(15,15) = 39750

Now, with    increasing k by 1 :
C(16 , 15) = 15000 + 50(16)^2 + 60(15)^2
C(16 , 15) = 41300

So, by increasing k by 1, C increased by 41300 - 39750 = 1550

Now, by increasing e by 1 :
C(15 , 16) = 15000 + 50(15)^2 + 60(16)^2
C(15 , 16) = 41610

So, by increasing e by 1, C increased by 41610 - 39750 = 1860

So, answers are :
a) The effect of increasing k by one unit is to increase C by $1550
b) The effect of increasing e by one unit is to increase C by $1860
c) If you are currently using carpenters and electricians to build a house, it would cost you "310 dollars less" to hire an additional carpenter ($ ) than to hire an additional electrician ($ ).

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