I have figured out most of this problem. I am having trouble with this question (part c) ONLY: Is the solution you found sensitive to changing food prices? By how much does the price of milk need to change to affect the solution? (How does the solution change?)

The campus dietitian for a small college is responsible for formulating a nutritious meal plan for students. For an evening meal, she feels that the following six meal-content requirements should be met:

The meal should be at least 900 calories

The meal should be at most 1500 calories

The meal should contain at least 4 milligrams of iron

The meal should have no more than 50 grams of fat

The meal should contain at least 26 grams of protein

The meal should contain no more than 50 grams of carbohydrates.

On a particular day, the food stock includes seven items that can be prepared and served for supper to meet these requirements. The cost per pound for each food item and the contribution to each of the nutritional requirements are given in the table below.

C) Is the solution you found sensitive to changing food prices? By how much does the price of milk need to change to affect the solution? (How does the solution change?)

Let X1 = the # of lbs. of milk per student

Let X2= the # of lbs. of ground meat per student

Ley X3 = the # of lbs. of chicken per student

Let X4 = the # of lbs. of fish per student

Let X5 = the # of lbs. of beans per student

Let x6 = the # of lbs. of spinach per student

Let X7 = = the # of lbs. of potatoes per student

Min. 0.6x1 + 2.35x2 + 1.15x3 + 2.25x4 + 0.58x5 + 1.17x6 + 0.33x7

Sub.To.

Calories: 295x1 + 1216x2 + 394x3 + 358 x4 +128x5 + 118x6 + 279 x7 >= 900

Calories: 295x1 + 1216x2 + 394x3 + 358 x4 +128x5 + 118x6 + 279 x7 <= 1500

Iron: 0.2x1 + 0.2x2 + 4.3x3 + 3.2x4 + 3.2x5 + 14.1x6 + 2.2x7 >= 4

Fat: 16x1 + 96x2 +9x3 + 0.5x4 +0.8x5 + 1.4x6 + 0.5x7 <= 50

Protein: 16x1 + 81x2 + 74x3 + 83x4 + 7x5 + 14x6 + 8x7 >= 26

Carbs: 22x1 + 28x5 + 19x6 + 63 x7 <= 50

X1,x2,x3,x4,x5.x6,x7 >= 0

Optimal Solution is:

x1 = 0 lbs., x2 = 0.4991 lbs., x3= 0.1728 lbs, x4= 0 lbs, x5= 0 lbs, x6= 0.1050 lbs, x7= 0.7620 lbs

Cost per meal = $1.7460 at Min.

Signs
	<						less than or equal to
	=						equals (You need to enter an apostrophe first.)
	>						greater than or equal to
Data											Results			Problem setup area
	x 1	x 2	x 3	x 4	x 5	x 6	x 7				LHS	Slack/Surplus
Objective	0.6	2.35	1.15	2.25	0.58	1.17	0.33	sign	RHS		1.74598			< constraints		> constraints
Constraint 1	295	1216	394	358	128	118	279	>	900		900	0		0	0	900	900
Constraint 2	295	1216	394	358	128	118	279	<	1500		900	600		900	1500	0	0
Constraint 3	0.2	0.2	4.3	3.2	3.2	14.1	2.2	>	4		4	0		0	0	4	4
Constraint 4	16	96	9	0.5	0.8	1.4	0.5	<	50		50	0		50	50	0	0
Constraint 5	16	81	74	83	7	14	8	>	26		60.78002	-34.78		0	0	60.78002	26
Constraint 6	22				28	19	63	<	50		50	0		50	50	0	0
Constraint 7	1							>	0		0	0		0	0	0	0
Constraint 8		1						>	0		0.499138	-0.49914		0	0	0.499138	0
Constraint 9			1					>	0		0.172751	-0.17275		0	0	0.172751	0
Constraint 10				1				>	0		0	0		0	0	0	0
Constraint 11					1			>	0		0	0		0	0	0	0
Constraint 12						1		>	0		0.105035	-0.10504		0	0	0.105035	0
Constraint 13							1	>	0		0.761973	-0.76197		0	0	0.761973	0
Results
Variables	0	0.499138	0.172751	0	0	0.105035	0.761973
Objective									1.74598