The cost to manufacture a product is proportional to the quantity produced, with a cost of $270000 dollars per day when 900 items are produced. The cost to store n items is proportional to the square of n, with a daily storage cost of $6480 dollars when 900 items are stored. In addition, there is a fixed daily cost of $4000. The total daily cost, C when producing and storing n items is the sum of production, storage and fixed costs.
Write a formula for Q as a function of n.
urgent!!
To find the formula for Q as a function of n, we need to consider the information given in the problem.
Let's break down the problem step by step:
1. The cost to manufacture a product is proportional to the quantity produced, with a cost of $270000 per day when 900 items are produced.
This means that for each item produced, the cost increases by $300 (270000/900). We can express this as a formula:
Cost per item = $270000/900 = $300.
As such, the total manufacturing cost for n items can be expressed as:
Manufacturing cost = $300 * n.
2. The cost to store n items is proportional to the square of n, with a daily storage cost of $6480 when 900 items are stored.
This means that the cost to store each item increases by $7.20 (6480/900), and the formula can be expressed as:
Storage cost per item = $7.20.
Thus, the total storage cost for n items can be expressed as:
Storage cost = $7.20 * n^2.
3. There is a fixed daily cost of $4000.
The fixed cost does not depend on the number of items produced or stored, so it can be directly added to the total cost.
Now, to find the total daily cost C when producing and storing n items, we can sum up the manufacturing cost, storage cost, and fixed cost:
C = Manufacturing cost + Storage cost + Fixed cost
C = ($300 * n) + ($7.20 * n^2) + $4000
Finally, we can rewrite the formula in terms of Q by substituting the given values:
Q = n - 900
Therefore, the formula for Q as a function of n is:
Q = (n - 900)