Anna Broderick is the dietician for the State University football team, and she is attempting to determine

Fantastic news! We've Found the answer you've been seeking!

Question:

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%)