Data
	Nutritional bounds
		Calories (Kcal)	Fat (g)	Sat fat (g)	Trans fat (g)	Cholesterol (mg)	Sodium (mg)	Carbs (g)	Fiber (g)	Sugar (g)	Protein (g)	Vitamin A (IU)	Vitamin C (mg)	Calcium (mg)	Iron (mg)
	Minimum	1900	30	0	0	0	1500	150	20	0	50	3000	300	1000	18
	Maximum	2200	75	25	300	300	2300	300	50	50	160	7000			40
Food	Serving size (g)	Calories (Kcal)	Fat (g)	Sat fat (g)	Trans fat (g)	Cholesterol (mg)	Sodium (mg)	Carbs (g)	Fiber (g)	Sugar (g)	Protein (g)	Vitamin A (IU)	Vitamin C (mg)	Calcium (mg)	Iron (mg)
Dounat	60	239	11	3	1	18	232	30	1	12	4	13.8	0.7	27.6	2.2
Bagel	57	145	1	0	1	0	289	30	2	1	6	2.3	0.1	0.8	1.8
Yogurt	125	119	0	0	0	2	72	24	0	24	6	15	0.9	190	0.1
Chili	216	190	8	3	0	25	1040	17	5	5	14	1250	36	80	1.4
Brocolli	140	49	1	0	0	0	57	10	5	2	3	2167	90.9	56	0.9
Apple	182	95	0	0	0	0	2	25	4	19	0	98.3	8.4	10.9	0.2
Oats	328	105	2	0	0	0	72	19	3	0	4	1000	0	98.5	8.2
Orange	140	69	0	0	0	0	1	18	3	12	1	346	82.8	60.2	0.2
Lentils	100	116	0	0	0	0	2	20	8	2	9	8	1.5	19	3.3
Carrots	28	10	0	0	0	0	22	2	1	1	0	3861	0.7	9	0.2
Brussel sprouts	78	28	0	0	0	0	16	6	2	1	2	604	48.4	28.1	0.9
Chicken	140	234	9	3	0	105	105	0	0	0	35	57.5	0	16.8	1.7
Bluberries	28	16	0	0	0	0	0	4	1	3	0	15.1	2.7	1.7	0.1
Spinach	180	41	0	0	0	0	126	7	4	1	5	18870	17.6	235	6.4
Banana	118	105	0	0	0	0	1	27	3	14	1	75.5	10.3	5.9	0.3
Milk 1%	244	102	2	2	0	12	107	13	0	13	8	478	0	290	0.1
Food	Cost per serving ($)	Excluded from diet
Dounat	0.85
Bagel	0.85
Yogurt	1.25
Chili	2.5
Brocolli	0.4
Apple	0.4
Oats	0.5
Orange	0.3
Lentils	0.35
Carrots	0.3
Brussel sprouts	0.5
Chicken	1.5
Bluberries	0.6
Spinach	0.3
Banana	0.3
Milk 1%	0.5

The optimal diet plan Based on a nutrition table, find the minimum-cost diet plan that contains total calories, fat, saturated fat, trans fat, cholesterol, sodium, carbohydrates, fibre, sugar, protein, vitamin A, vitamin C, calcium and iron that are within a given range. All the data is provided in the excel file Data_file.xIsx. Specifically, the data includes a nutrition table, nutrition bounds, and price per serving. For example, a 60g serving size of donut costs $0.85, and contains 239Kcal calories, 11g fat, 3g saturate fat, 1g trans fat, 18mg cholesterol, 232mg sodium, 30g carbs, 1g fiber, 12g sugar, 4g protein, 13.8U vitamin A, 0.7mg vitamin C, 27.6mg calcium, and 2.2mg iron. An optimal diet plan should consist of at least 1900Kcal calories and not more than 2200Kcal, maximum 300mg of cholesterol (there is no minimum requirement), minimum 300mg vitamin C (there is no maximum requirement), and so on. 1. What is the objective? Do you minimize or maximize the objective? 2. What are the decision variables? 3. Built a model and find the optimal diet plan based on the data provided in the excel file Data_file.xlsx. What is the optimal value of your objective? 4. What is the optimal diet plan? 5. According to your solution, give an example of a binding constraint. Explain why it is binding. 6. Generate a sensitivity analysis report and answer the following questions: a. What is the reduced cost for Chili? Why did we receive this value? b. What is the shadow price of the minimum total calories' constraint? What does it mean? Give an explanation in words. 7. Use the function IF to fill out cells C29:C44 of all the food items that are excluded from your diet. 8. What is the economic value of raising the maximum calories by another 100 calories? What method did you use to answer the