BDM midterm
SOLUTIONS
1) Ralph Edmund loves steak and potatoes. Therefore, he has decided to go on a steady diet of only these two foods for all his meals. Ralph realizes that this is not 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 and costs data:
Grams of Ingredient Per Serving.
Ingredient
Steak
Potato Daily Requirement (g)
Carbs
5
15
>=50
Protein
20
5
>=40
Fat
15
2
>=60
Cost/Serving
$4
$2
Ralph wishes to determine the number of daily servings of steak and potatoes that will meet these requirements at a minimum cost. Formulate the Linear programming model for this problem.
Let
S = servings of steak in diet
P = servings of potatoes in the diet
Minimize C = $4S + $2P, subject to
5S + 15P ≥ 50
20S + 5P ≥ 40
15S + 2P >= 60 and S ≥ 0, P ≥ 0.
2) The Oak Works is a family owned business that makes hand crafted dining room tables and chairs.
They obtain the oak from a local tree farm, which ships them 2500 pounds of oak each month. Each table uses 50 pounds of oak while each chair uses 25 pounds of oak. The family builds all the furniture itself and has 480 hours of labour available each month. Each table or chair requires 6 hours of labour.
Each table nets Oak Works $400 in profit, while each chair nets them $100 in profit. Since chairs are often sold with tables they want to produce at least twice as many chairs as tables. Formula a linear program to maximize profit.
Let
T = # of tables to produce
C = # of chairs to produce
Maximize P = $400T + $100C subject to
50T + 25C≤ 2,500 -> Raw Material Constraint
6T + 6C ≤ 480 -> Labour Constraint
C ≥ 2T -> Management Constraint and T ≥ 0, C ≥ 0 -> Non Negativity Constraint
3) Let xij = number of units produced at plant i of product j (i = 1, 2, 3; j = L, M, S).
Maximize Profit = $420(x1L + x2L +
1) Ralph Edmund loves steak and potatoes. Therefore, he has decided to go on a steady diet of only these two foods for all his meals. Ralph realizes that this is not 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 and costs data:
Grams of Ingredient Per Serving.
Ingredient
Steak
Potato Daily Requirement (g)
Carbs
5
15
>=50
Protein
20
5
>=40
Fat
15
2
>=60
Cost/Serving
$4
$2
Ralph wishes to determine the number of daily servings of steak and potatoes that will meet these requirements at a minimum cost. Formulate the Linear programming model for this problem.
Let
S = servings of steak in diet
P = servings of potatoes in the diet
Minimize C = $4S + $2P, subject to
5S + 15P ≥ 50
20S + 5P ≥ 40
15S + 2P >= 60 and S ≥ 0, P ≥ 0.
2) The Oak Works is a family owned business that makes hand crafted dining room tables and chairs.
They obtain the oak from a local tree farm, which ships them 2500 pounds of oak each month. Each table uses 50 pounds of oak while each chair uses 25 pounds of oak. The family builds all the furniture itself and has 480 hours of labour available each month. Each table or chair requires 6 hours of labour.
Each table nets Oak Works $400 in profit, while each chair nets them $100 in profit. Since chairs are often sold with tables they want to produce at least twice as many chairs as tables. Formula a linear program to maximize profit.
Let
T = # of tables to produce
C = # of chairs to produce
Maximize P = $400T + $100C subject to
50T + 25C≤ 2,500 -> Raw Material Constraint
6T + 6C ≤ 480 -> Labour Constraint
C ≥ 2T -> Management Constraint and T ≥ 0, C ≥ 0 -> Non Negativity Constraint
3) Let xij = number of units produced at plant i of product j (i = 1, 2, 3; j = L, M, S).
Maximize Profit = $420(x1L + x2L +