A school is trying to determine a nutritional diet to feed its students.The 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.Let K and T be the number pounds of kidney beans and tofu to be purchased.Which of the following is the optimal solution values of the decision variables? $$\begin{array} { | l | l | l | l | }
\hline \text { Nutrient } & \begin{array} { l }
\text { Kidney } \
\text { Besns }
\end{array} & \text { Tofu } & \begin{array} { l }
\text { Minimum } \
\text { Deily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \text { Calcium in units per pound } & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \text { Calories in units per pound } & 3 & 9 & 18 \
\hline
\end{array}$$
A)K=1,T =3
B)K=3,T =1
C)K=2,T=2
D)K=4,T=1

Question

A school is trying to determine a nutritional diet to feed its students.The 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.Let K and T be the number pounds of kidney beans and tofu to be purchased.Which of the following is the optimal solution values of the decision variables? $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Besns }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum } \
\text { Deily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \text { Calcium in units per pound } & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \text { Calories in units per pound } & 3 & 9 & 18 \
\hline
\end{array}$$
A)K=1,T =3
B)K=3,T =1
C)K=2,T=2
D)K=4,T=1

Quizplus · Accepted Answer

To meet the minimum daily requirements at the lowest cost, we need to solve a linear programming problem. The constraints are based on calcium, protein, and calories. By analyzing the constraints:- For calcium: $15K + 6T \geq 30$- For protein: $10K + 10T \geq 40$- For calories: $3K + 9T \geq 18$Option B, $K=3, T=1$, satisfies all the minimum requirements:- Calcium: $15(3) + 6(1) = 45 + 6 = 51$, which is greater than 30.- Protein: $10(3) + 10(1) = 30 + 10 = 40$, which meets the requirement.- Calories: $3(3) + 9(1) = 9 + 9 = 18$, which meets the requirement.And considering the cost, $3K$ at $0.90 and $1T$ at $1.50 minimizes the cost while meeting all nutritional requirements.

A School Is Trying to Determine a Nutritional Diet to Feed