Question #6a90d

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Answer 1 · 2017-05-22T13:57:57

If $60$ items per day are produced, the unit cost is minimum, i.e.,

$$400.$

$C(x)=x^2-120x+4000.$ Completing the square, we get,

$C(x)=x^2-2*60x+60^2-60^2+4000, i.e.,$

$C(x)=(x-60)^2+4000-3600=(x-60)^2+400,$

Since, $AA x in RR, (x-60)^2 >=0, C(x) >=400,$ which means that,

The Minimum Unit Cost is $$400.$

Further, for this minimum unit cost, if $x$ items per day are produced, then,

$C(x)=400 rArr (x-60)^2+400=400 rArr x=60.$

Thus, if daily $60$ items are produced, the unit cost is minimum, i.e.,

$$400.$

Enjoy Maths.!