Question: The demand and cost function of a particular brand of lawn mower are given, respectively, by \(p\left( x \right)=150-0.03x\) and \(c\left( x \right)=1425+120x\), where x is the number of lawn mowers that can be sold at a price p and \(c\left( x \right)\) is the total cost of producing x lawn movers

(a) Find \(\frac{dp}{dx}\), and interpret what does this symbol means

(b) Find the revenue function in terms of x.

(c) Find \(R'\left( 450 \right)\) and \(R'\left( 700 \right)\) and interpret the results

(d) Determine the break-even points

(e) Find the profit function in terms of x

(f) Find \(P'\left( 450 \right)\) and \(P'\left( 700 \right)\) and interpret the results.

(g) Determine the price elasticity of demand when the price is set at $120 per lawnmower and at $70 per lawnmower