Sum is from application of calculus in commerce and economics - Maths - Application of Derivatives

Question

Sum is from application of calculus in commerce and economics

Ankita Agarwal · Accepted Answer

Dear Student,

Selling price of 1 item =Rs
(330−x)(Given) Selling price of x items =Rs
 x(330−x) Cost price of x items =Rs
(x2+10x−12) Profit = Selling price − Cost price ⇒ Profit =(330x−x2)−(x2+10x−12)                  =320x−2x2+12 Now, P=−2x2+320x+12 Differentiating above equation, we get dPdx​=−4x+320 Differentiating againg w
r t
 x, we get d2Pdx2​=−4⇒ Always negative To maximize the profit, dpdx​=0−4x+320=0x=−320-4​=80 ∵d2Pdx2​<0 for any value of x, thus 80 items must be sold so that his profit is maximum

Regards