Question

A paint company has a specific type of interior paint which costs $5.55 to produce each unit. The company also has a fixed cost of $15,000 per month. The price function for this paint is p 42 0.01q, where p is the price at which exactly q units are sold. The company must make at least 1000 units to remain competitive. 1. Find the minimum total cost for one month 2. Find the maximum revenue for one month. 3. Find the maximum profit for one month.

Answer 1

Minimum total cost = $20550

maximum revenue $44,100

Explanation:

Given data:

Production cost $5.55 per unit

Fixed cost = $15000 per month

Price, p = 42-0.01 q

where. q represent number of unit produced

revenue can be wriiten as

p.q = 42q - 0.01q^2

1) from information 1000 unit has to produced therefore

total cost = 15000 + 5.55×1000 = $20550

Minimum total cost = $20550

2) Revenue = 42q - 0.01q^2

`(d revenue)/(dq) = 42q - 2* 0.01q = 0`

therefore for maximum revenue q is = 2100

so, maximum revenue
`=  4.2 * 2100 - 0.01(2100)^2`

= $44,100