Anna Broderick is the dietician for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines for each lunch serving:

 Between 1,300 and 2,100 calories

 At least 4 mg of iron

 At least 15 but no more than 55g of fat

 At least 30g of protein

 At least 60g of carbohydrates

 No more than 35 mg of cholesterol

She selects the menu from seven basic food items, as follows, with the nutritional contributions per pound and the cost as given:

The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.

a. Formulate a linear programming model for this problem and solve it.

b. If a serving of each of the food items (other than milk) was limited to no more than a half-pound, what effect would this have on the solution?

Anna Broderick Lunch Menu
				Calories	Iron	Protein	Carbo-hydrates	Fat (g/lb.)	Cholesterol	Cost
				(per lb.)	(mg/lb.)	(g/lb.)	(g/lb.)		(mg/lb.)
										$/lb.
			Chicken	500	4.2	17	0	30	180	0.85
			Fish	480	3.1	85	0	5	90	3.35
			Ground beef	840	0.25	82	0	75	350	2.45
			Dried beans	590	3.2	10	30	3	0	0.85
			Lettuce	40	0.4	6	0	0	0	0.7
			Potatoes	450	2.25	10	70	0	0	0.45
			Milk (2%)	220	0.2	16	22	10	20	0.82
	Constraints			>=	>=	>=	>=	>=	<=
				1300	4	30	60	15	35
				<=				<=
				2100				55
(a)	Objective		Minimize Cost ($)
(b)	if a serving of each of the food items (other than milk) was limited to no more than a half-pound, what effect would this have on the solution?
	Decision Variables		Chicken		<=	0.5
			Fish		<=	0.5
			Ground beef		<=	0.5
			Dried beans		<=	0.5
			Lettuce		<=	0.5
			Potatoes		<=	0.5
			Milk (2%)

Calories Iron Protein Carbo- Fat Cholesterol Cost (per Ib.) (mg/lb.) (g/lb.) hydrates (g/lb.) (mg/lb) (S/lb.) (g/lb.) Chicken 500 4.2 17 30 180 0.85 Fish 480 3.1 85 90 3.35 Ground beef 840 0.25 82 75 350 2.45 Dried beans 590 3.2 10 30 3 0.85 Lettuce 40 0.4 6. 0.70 Potatoes 450 2.25 10 70 0.45 Milk (2%) 220 0.2 16 22 10 20 0.82