On a recent doctor’s visit, you have been told that you must watch your calorie intake and must make sure you get enough vitamin E in your diet.
A:
You have decided that, to make life simple, you will from now on eat only steak and carrots. A nice steak has 250 calories and 10 units of vitamins, and a serving of carrots has 100 calories and 30 units of vitamins Your doctor’s instructions are that you must eat no more than 2000 calories and consume at least 150 units of vitamins per day.
(a) In a graph with “servings of carrots” on the horizontal and steak on the vertical axis, illustrate all combinations of carrots and steaks that make up a 2000 calorie a day diet.
(b) On the same graph, illustrate all the combinations of carrots and steaks that provide exactly 150 units of vitamins.
(c) On this graph, shade in the bundles of carrots and steaks that satisfy both of your doctor’s requirements.
(d) Now suppose you can buy a serving of carrots for $2 and a steak for $6. You have $26 per day in your food budget. In your graph, illustrate your budget constraint. If you love steak and don’t mind eating or not eating carrots, what bundle will you choose (assuming you take your doctor’s instructions seriously)?
B:
Continue with the scenario as described in part A.
(a) Define the line you drew in A (a) mathematically.
(b) Define the line you drew in A (b) mathematically.