Question

George loves pork and carrot. Therefore, he has decided to go on a steady diet of only these two foods (plus some liquids and vitamin and supplements) for all his meals. George realizes that this isn’t the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional requirement. He has obtained the following nutritional and cost information.

	Grams of Ingredient per Serving
	Pork	Carrot	Daily Requirement
Carbohydrates	6	17	≥45
Protein	25	5	≥48
Fat	11	3	≤72
Cost per Serving	$6	$9

George wishes to determine the number of daily servings (may be fractional) of pork and carrot that will meet this requirement at a minimum cost.

(a) Identify decision variables, objective function, and constraints and explain them in words, using at least 100 words

(b) Formulate a mathematical linear programming model using equations. Make sure you provide the exact descriptions of each variable and mathematical notations shown in the assignment guideline ppt.

(c) Solve a linear programming model for this problem on a spreadsheet, and interpret the results (meaning what is the optimal amount of daily serving for pork and carrot, and what is the minimum cost at the optimal servings of pork and carrot?), using at least 100 words

Answer 1

Therefore, the optimal daily servings of pork and carrot are :

1.50 servings of pork & 2.12 servings of carrot.

Mimimum cost is = $28.05.