A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | }
\hline \text { Nutrient } & \begin{array} { l }
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l }
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l }
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l }
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,what is the cost of the nutritional diet?
A)$4.20
B)$3.55
C)$7.30
D)$8.25

Question

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l } 
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,what is the cost of the nutritional diet?
A)$4.20
B)$3.55
C)$7.30
D)$8.25

Quizplus · Accepted Answer

Let x be the amount of kidney beans in pounds and y be the amount of tofu in pounds.

The objective function to be minimized is:
0.9x + 1.5y (cost)

The constraints are:
15x + 6y >= 30 (calcium)
10x + 10y >= 40 (protein)
3x + 9y >= 18 (calories)
x, y >= 0 (non-negativity)

Using a linear programming solver, the optimum solution is x = 0.8 and y = 1.6, with a cost of $4.20. Therefore, the school should offer 0.8 pounds of kidney beans and 1.6 pounds of tofu to its students to meet the nutritional requirements at the lowest cost.

A School Is Trying to Determine a Nutritional Diet to Feed