Question

The sales function is S(x)= 20 + 150x² - 4x³

^{x represents thousands of dollars spent on advertising, 0< x<40, and S is in thousands of dollars. Find the point of diminishing returns (inflection point.) Determine the amount spent on advertising, and sales in dollars. (give both coordinates.)}

^{Point of diminishing returns:}

^{Amount spend on advertising:}

^{Sales in dollars:} ​​​​​​​

Answer 1

Given sales function S(X) = 20 +15012_4x3 where oln240 represent thousands of dollar spent on advertising S'(x) = (20+150x2 - 4x3) = 0 + 300x -12% 2 Now S'lm) – 300% -12%? Now 5"( d - (3007 –12x2) = 300 - 24x dn S"(=0 for point of diminishing returns '. 300 – 24x = 0 x = 12.5 at XS 12.5, 5(12:5) = 20 +150112.592-4(12-5)3 =15645 point of diminishing diminiehing return is (~, S(x)) = (12.5, 15645) so Amount Hence on spent Advertising is = dollar X = 12.5 thougande [ 12 112 500 and dollar sales in dollar I 15645000 sales is ( Because 15695 thousands of dollar) 2=12.5 at Answer, like please thumbs up thumbs up thank you If you