Answer to Question #146944 in Algebra for Saba

Question

In manufacturing a medical equipment, a firm incurs costs of two types. Fixed annual costs of $ 155,000 are incurred regardless of the number of units produced. In addition, each unit produced costs the firm $5. If C equals total annual cost in dollars and x equals the number of units produced during a year;
a) Develop the function C = f(x) which expresses annual cost.
b) Calculate f(280,000)? What does f(280,000) represent?
c) State the restricted domain and restricted range of the function if maximum production
capacity is 850,000 units per year

Answer 1

a)

$$C(x)=155000+5x$$

b)

$$C(280000)=155000+5(280000)=1555000$$

It is needed $1,555,000 to produce 280,000 units.

c)

$Domain \ [ 0, 850000]$

$$C(850000)=155000+5(850000)=4405000$$

$Range\ [155000, 4405000]$