MATH SOLVE

4 months ago

Q:
# 5. A factory produces lemon-scented widgets. You know that each unit is cheaper, the moreyou produce. But you also know that costs will eventually go up if you make too manywidgets, due to the costs of storage of the overstock. The guy in accounting says that yourcost for producing.x thousands of units a day can be approximated by the formula ( = 0.04x2 β8.504x + 25302. Find the daily production level that will minimize your costs.

Accepted Solution

A:

Answer: 106300 units per day.Step-by-step explanation:The cost of producing x thousands of units of lemon-scented widgets in a day is given by the formula C=0.04xΒ² - 8.504x + 25302 ....... (1), where x is the number of units produced in thousands.
We are asked to find the daily production level that will minimize the cost.
Now, condition for minimum cost is [tex]\frac{dC}{dx} =0[/tex]
So, from equation (1), [tex]\frac{dC}{dx} =0.08x-8.504 =0[/tex]
β x =106.3
Therefore, the cost will be minimized when daily production is 106300 units. (Answer)