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Question
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.
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Solution
Total cost C(x) = Processing cost + labour cost
C(x) = x2 + 150 - 54x
C(x) = x2 - 54x + 150
`("dc")/("dx")` = 2x - 54
Total cost is decreasing
If `("dc")/("dx")`< 0
i.e if 2x - 54 < 0
i.e if 2x < 54
i.e if x < 27
Total cost C is decreasing for x < 27.
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