Write a formula for Q as a function of n.

Question

The cost to manufacture a product is proportional to the quantity produced, with a cost of $80000 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 $1000. 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.

Answer 1

MANUFACTURING COST:

cost to manufacture a product is proportional

to the quantity produced:

M(n) = kn

 

$80000 dollars per day when 800 items are produced

80,000 = 800k

k = 80,000/800 = 100

 

M(n) = 100n

 

STORAGE COST:

cost to store n items is proportional to the square of n

S(n) = kn²

 

daily storage cost of $6400 dollars when 800 items are stored

6400 = k(800²)

6400 = 640,000k

k = 6400/640,000 = 0.01

 

S(n) = 0.01n²

 

fixed daily cost of $1000

 

Q(n) = M(n) + S(n) + 1000

 

Q(n) = 100n + 0.01n² + 1000