Solution:
In linear programming, Capital budgeting models to minimize the total capital cost.
The solutions from the model are used to decide the best combination of capital resources and best times to start and finish projects and to determine the net capital cost.
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$(A)$ $f (2)<1-\log _{ e } 2$ $(B)$ $f (2)>1-\log _{ e } 2$ $(C)$ $g(1)>1-\log _e 2$ $(D)$ $g(1)<1-\log _e 2$
$f_1(x)=\int_0^x \prod_{j=1}^{21}( t - j )^{ j } dt , x >0$
and
$f_2(x)=98(x-1)^{50}-600(x-1)^{39}+2450, x>0,$
where, for any positive integer $n$ and real numbers $a _1, a _2, \ldots, a _{ n }, \prod_{i=1}^{ n } a _i$ denotes the product of $a _1, a _2, \ldots, a _{ n }$. Let $m _i$ and $n _i$, respectively, denote the number of points of local minima and the number of points of local maxima of function $f_i, i=1,2$, in the interval $(0, \infty)$
($2$) The value of $2 m_1+3 n_1+m_1 n_1$ is. . . . . .
($2$) The value of $6 m _2+4 n _2+8 m _2 n _2$ is. . . . . .
Give the answer or quetion ($1$) and ($2$)