A girl wants to lose weight, but in the meantime, she does not want to be in lack of certain nutritions. Find her a minimum calorie diet that contains at least 800 mg of calcium, 55 grams of protein, and 200 grams of carbohydrates
In order to avoid monotony, she decides to eat at most 5 units of each food type. She likes eating yogurt with apples, so any time she eats a yogurt, she eats an apple with it. She does not want to eat baked beans and roast chicken on the same day, so she decides that she will only eat from one of them.
The point is, we need to decide:
- What food she will eat
- How many items of it to eat
so that to satisfy nutrition needs and minimize total calories.
That’s why the above two points can be our variables.
VAR:
x_i: =1 if she eats i, =0 if not (i=1..5) binary
b_i = units she eats for i integer
PARAM:
c_i: calcium in i
p_i: protein in i
k_i: carb in i
z_i: calories in i
CONSTRAINTS:
she decides to eat at most 5 units of each food type
0 ≤ b_i ≤5 for all i
any time she eats a yogurt, she eats an apple
b_2 * x_2 ≤ b_1 * x_1
She does not want to eat baked beans and roast chicken on the same day, so she decides that she will only eat from one of them
x_3 + x_5 = 1
she does not want to be in lack of certain nutritions
sum_i(b_i * x_i *c_i) ≥ 800
sum_i(b_i * x_i *p_i) ≥ 55
sum_i(b_i * x_i *k_i) ≥ 200
OBJ:
minimize sum_i (b_i * x_i *z_i)
Solve in XPRESS
So, she will eat 5 apples, 5 yogurts, 5 baked beans, and 4 boiled eggs each day to satisfy her nutrition needs and she will get minimum calories: 1687 kcal from this plan.
