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Jack has $50 in his wallet. A candy bar costs $2, and an energy drink costs $4. Draw his budget line. i) Suppose the store has a discount on candy bars. The first five candy bars sell for $1 each. Any additional candy bars will be the original price. What will be Jack's new budget line? Compare it with his original. ii) The store now has a promotion on energy drinks. After purchasing 2 cans of energy drink, the store will give a $1 discount on any additional energy drinks. What will be his new budget line? Compare it with the original.
Jack has $50. How many candy bars can Jack buy with $50 if he only buys candy bars? He can buy 25 bars, because each costs $2. (50/2 = 25) Alternatively, how many energy drinks can Jack buy if he only buys energy drinks? He can buy 12.5, because each energy drink costs $4. (50/4 = 12.5) |dw:1435311184806:dw| |dw:1435311278822:dw|
Next, begin the analysis the same way except now we have some new information: the first 5 bars have a lower price--so we know that there will be a "kink" in the budget line.
How many bars can Jack buy now, if the first 5 only cost $1, but after that bars cost $2. He can buy 5 bars for $1. This leaves us with $45. How many bars can he buy with $45 if each costs $2... He can buy 45/2 = 22.5 more bars. So the maximum is the first 5 plus the next 22.5, or 27.5 total.
How many drinks can Jack buy if he buys 5 candy bars at $1 each? He has $45 to spend on drinks in that case, and 45/4 = 11.25, so the kink is at the position (x, y) = (11.25, 5).
The drawing doesn't show the kink very well, sorry
Anyway, keep doing the same thing for the rest of the problem, should be easy.