Question

question 15
a company makes tables (t) and chairs (c).
constraints:
4t + 2c ≤ 40
t + c ≤ 15
t ≥ 0
c ≥ 0
profit equation: p=30t+20c
choose the combination that maximizes profit.

○ t=8 c=7
○ t=0 c=15
○ t=5 c=10
○ t=10 c=0

Explanation:

Step1: Check Feasibility of Each Option

• For \( T = 8, C = 7 \):
• Check \( 4T + 2C \): \( 4(8)+2(7)=32 + 14 = 46 \). Since \( 46>40 \), this option violates the first constraint.
• For \( T = 0, C = 15 \):
• Check \( 4T + 2C \): \( 4(0)+2(15)=30 \leq 40 \).
• Check \( T + C \): \( 0 + 15 = 15 \leq 15 \). Both constraints are satisfied.
• For \( T = 5, C = 10 \):
• Check \( 4T + 2C \): \( 4(5)+2(10)=20 + 20 = 40 \leq 40 \).
• Check \( T + C \): \( 5 + 10 = 15 \leq 15 \). Both constraints are satisfied.
• For \( T = 10, C = 0 \):
• Check \( 4T + 2C \): \( 4(10)+2(0)=40 \leq 40 \).
• Check \( T + C \): \( 10 + 0 = 10 \leq 15 \). Both constraints are satisfied.

Step2: Calculate Profit for Feasible Options

• For \( T = 0, C = 15 \): \( P = 30(0)+20(15)=300 \).
• For \( T = 5, C = 10 \): \( P = 30(5)+20(10)=150 + 200 = 350 \).
• For \( T = 10, C = 0 \): \( P = 30(10)+20(0)=300 \).

Answer:

\( T = 5, C = 10 \) (The option with \( T = 5 \) and \( C = 10 \))