Alejandro makes $$180$ each week at a part time job as a cashier. He spends his weekly income on gallons of chocolate milk and boxes of cereal. Gallons of chocolate milk cost $$10$ per gallon and boxes of cereal cost $$6$ per box.

a$.$ Graph Alejandro's budget constraint and label it $B{C}_1.$ Label boxes of cereal on the $x$ axis and gallons of chocolate milk on the $Y$ axis.

b$.$ Alejandro clips a coupon good for $3$ free boxes of cereal. Show the effect of this change on Alejandro's budget constraint, labeling it $B{C}_2.$ Is Alejandro's opportunity cost constant along the budget constraint? Explain.

c$.$ Stores are having a Valentines Day promotion: buy the first $3$ boxes of cereal at regular price; and all boxes after the third box are half$-$off $(50\%$ of the original price$).$ Show the effect of this change on Alejandro's budget constraint, labeling it $B{C}_3.$ Is Alejandro's opportunity cost constant along the budget constraint? Explain.