(a)[4]
Sima sells $x$ biscuits and $y$ cakes. (i) She sells no fewer than 100 biscuits. (ii) She sells no fewer than 120 cakes. (iii) The total number of items she sells is at most 300. (iv) Each biscuit gives $40$ cents profit and each cake $80$ cents. Her total profit is at least $160$. Show that $x + 2y \ge 400$.
(b)[6]
On the grid, sketch four lines to represent the inequalities and shade the regions that are not wanted.
(c)[2]
Calculate Sima’s greatest profit. Give your answer in dollars.