Arithmetic and Composition

Question

The cost to manufacture a product is proportional to the quantity produced, with a cost of $200000 dollars per day when 800 items are produced. The cost to store n items is proportional to the square of n, with a daily storage cost of $6400 dollars when 800 items are stored. In addition, there is a fixed daily cost of $2000. 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.
Q=

Answer 1

First of all, I think you mistyped Q and C, I'll assume those two are the same.

 

From the last statement, you are aiming for an equation:

 

Total Daily Cost = Production + Storage + Fixed Cost, Let's say:

 

C = P + S + F      (general equation)

 

1. Let's check the production first:

 

The production cost (P) is (directly) proportional to the number of items (n):

 

P = kn. They gave you a scenario, where C = 200000 when n = 800:

 

200000 = k(800), therefore k = 250, THEREFORE: P = 250n

 

2. The storage:

 

They said that the storage cost (S) is (directly proportional) to the square of the number of items (n):

 

S = kn². Again they gave you a scenario, where S = 6400 when n = 800:

 

6400 = k(800²), therefore k = 1/100, THEREFORE: S = n²/100

 

3. The fixed cost is simply the value given since it's constant. Imagine this in real life, of course the fixed cost is constant, it won't change, hence the word FIXED so:

 

F = 2000

 

Going back to the general equation C = P + S + F, it would just be:

 

C = 250n + (n²/100) + 2000