Question

2.19 Billy Bob wants to gain some weight so that he can play football. Billy eats only milkshakes and spinach. Milkshakes cost him $1 each and spinach costs $2 per serving. A milkshake has 850 calories and a serving of spinach has 200 calories. Billy Bob never spends more than $20 a day on food and he always consumes at least 8000 calories per day. Which of the following is necessarily true? (a) Billy Bob consumes at least 9 milkshakes a day. (b) Billy Bob never consumes more than 6 servings of spinach a day . (c) Billy Bob never consumes positive amounts of both goods. (d) Billy Bob consumes only milkshakes. (e) None of the above. Answer is B. Please show me a full working solution.

Answer 1

Option (b) Billy Bob never consumes more than 6 servings of spinanch a day.

This is because 1 serving of spinach has 200 calories and he always consumes a total of 8000 calories. Which means,

6 servings of spinach = 200 * 6 = 1200 calories.

1 serving of milkshake has 850 calories and again, if I repeat he consumes a totoal of 8000 calories in total.

For a total of 8000 calories, he has to consume (8000 - 1200) = 6800 calories from milkshake.

So, for 6800 calories, he has to consume 6800/850 = 8 servings of milkshake.

Now, he also has the budget limit of $20 a day on food.

So, 1 serving of spinach = $2

6 sevings of spinach = 2*6 = $12.

1 serving of milkshake = $1

8 servings of milkshake = $1 * 8 = $8

Total budget = $12 + $8 = $20.

If he would have consumed more than 6 servings of spinach, for example 7 servings of spinach then, it would have cost him $7*2 = $14 only for spinach and then he would have to consume 7 servings of milkshake for his limited budget. This combination would not have fetched him his required 8000 calories per day. This is why he never consumes more than 6 servings of spinach a day.