**Finding the Optimum Point**

1a) The local "Supplies 'n' Vittals" have two top sellers: "Froggatt's Lumpy Sprout Ketchup" and "Froggatt's Bone-tingling Fireball Soup" (not available in all areas). The sales of these products are limited by the following factors:

1) Following an unusually good growing season, a severe shortage of suitably lumpy sprouts has meant total sales of the Ketchup are rationed to 200 bottles per month.

2) The local Health Department have limited the combined sales of these two Froggatt's products to 250 items per month.

3) Froggatt's themselves, ever keen to preserve their more traditional health products insist that all retailers must sell at least as much Ketchup as Bone-tingling Soup.

Using L to represent the number of bottles of Lumpy Sprout Ketchup sold and B to represent the number of tins of Bone-tingling Fireball Soup, write down three inequalities.

1b) The prices of the above products are £2 per bottle of Lumpy Sprout Ketchup, and £1.50 per tin of Bone-tingling Fireball Soup. Find the maximum possible income, and say how many of each will be sold per month.

1c) Do the question again but with these new figures: The Bone-Tingling Soup goes up to £3 per tin, and the total monthly sales may now go up to 300 items.

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