(Solved): What is the shortest possible length of the line segment that is cut off by the first quadrant and ...

What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve \( y=\frac{5}{x} \) at some point? A manufacturer has been selling 1000 flat-screen TVs a week at \( \$ 350 \) each. A market survey indicates that for each \( \$ 10 \) rebate offered to the buyer, the number of TVs sold will increase by 100 per week. (a) Find the demand function (price \( p \) as a function of units sold \( x \) ). \( p(x)= \) (b) How large a rebate should the company offer the buyer in order to maximize its revenue? \$ \( \boldsymbol{x} \) (c) If its weekly cost function is \( C(x)=72,000+150 x \), how should the manufacturer set the size of the rebate in order to maximize its profit?