Question

5. A factory produces lemon-scented widgets. You know that each unit is cheaper, the more

you produce. But you also know that costs will eventually go up if you make too many
widgets, due to the costs of storage of the overstock. The guy in accounting says that your
cost for producing.x thousands of units a day can be approximated by the formula ( = 0.04x2 –
8.504x + 25302. Find the daily production level that will minimize your costs.

Answer 1

106300 units per day.

Explanation:

The cost of producing x thousands of units of lemon-scented widgets in a day is given by the formula C=0.04x² - 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
`(dC)/(dx) =0`

So, from equation (1),
`(dC)/(dx) =0.08x-8.504 =0`

⇒ x =106.3

Therefore, the cost will be minimized when daily production is 106300 units. (Answer)