(1) Let x be the quantity of pens. The total cost of producing pens is 70+2x, where x is the quantity of pens produced. You want to sell the pens at...

(1) Let x be the quantity of pens. The total cost of producing pens is 70+2x, where x is the quantity of pens produced. You want to sell the pens at a price of 14-0.1x per pen. (i) What is the revenue function? [2] (ii) What is the profit function? [2] (iii) What is the domain of the revenue function and profit function? [3] (iv) What is the break even point? [2] (v) What quantity of pens must be sold to make a loss? [2] (vi) How many pens must I sell to make a profit of $50? [2] (vii) Show that the maximum profit is $290. [2] (viii) My selling price can be written as b-ax. If b = 14 and a = 0.1, my selling price becomes 14-0.1x (as in the original question). If I want my profit be $400 and want to keep b = 14, what must the maximum value of a? [4] (ix) If I want my profit to be $300 and want to keep a = 0.1, what must be the minimum value of b? [4] (x) Show that to break even, b must be more than 2. [2]