Question

The cost to manufacture a product is proportional to the quantity produced, with a cost of $35000 dollars per day when 700 items are produced. The cost to store n items is proportional to the square of n, with a daily storage cost of $3430 dollars when 700 items are stored. In addition, there is a fixed daily cost of $7000. The total daily cost, T when producing and storing n items is the sum of production, storage and fixed costs.
Write a formula for T as a function of n.

Answer 1

Solution :

$T_1$ = k.n (cost proportional to quantity)

35000 = k . 700

k = $\frac{35000}{700}$

  = 50

So $T_1$ = 50 n

Now $T_2=Pn^2$     (cost proportional to square of n)

$3430= P(700)^2$

3430 = 490000 P

$P = \frac{3430}{490000}$

$P = \frac{7}{1000}$

$T_2=\frac{7}{1000}n^2$

Now, $T_3= 7000$   (fixed)

Therefore,

Total, $T=T_1+T_2+T_3$

$T=50n+\frac{7}{1000}n^2+7000$

$T=0.007n^2+50n+7000$