有冇人知依題數點計呀?

15(a)

Let c=aA+bA*/n ,where a and b are non-zero constants.

When A=50 and n=500 ,C=350 ,we have

50a+(50*)b/500=350
10a+b=70 --------------------------(1)

When A=20 and n=400 ,C=100 ,we have

20a+(20*)b/400=100
20a+b=100 -------------------------(2)

Solving (1) and (2) ,we have
a=3 and b=40

Thus ,we have C=3A+40A*/n.


15(b)
(i)

Note that P=8A-(3A+40A*/n)

Thus ,we have P=5A-40A*/n

(ii)

When P:n=5:32

5n/32=5A-40A*/n
256A*-32An+n*=0
(16A-n)*=0
Thus ,we have A:n=1:16

(iii)

When n=500 and P=100 ,we have 5A-40A*/500=100

So, we have 2A*-125A+2500=0\

delta(三角形似的希臘文)=(-125)*-4(2)(2500)
=-4375
<0
Thus ,it is impossible to make a profit of $100

(iv)

When n=400 ,


P=5A-40A*/400
=5A-A*/10
=-1/10(A*-50A)
=-1/10(A*-50A+25*-25*)
=-1/10(A-25)*+125/2

Thus ,the greatest profit is $62.5