# Step-by-Step Solution Let's break down the cost calculation for each option over 12 years: --- ## **Step 1: Calculate Annual Energy Consumption** **Operating hours per year:** - 12 hours/day × 365 days/year = **4,380 hours/year** ### **Option A: Standard Escalator** - Energy used per hour: **12 kWh** - Annual energy use: \( 12 \text{ kWh} × 4,380 \text{ hours} = 52,560 \text{ kWh/year} \) ### **Option B: High-Efficiency Escalator** - Energy used per hour: **8 kWh** - Annual energy use: \( 8 \text{ kWh} × 4,380 \text{ hours} = 35,040 \text{ kWh/year} \) --- ## **Step 2: Calculate Annual Energy Cost** **Electricity rate = ₱12 per kWh** ### **Option A** - Annual cost: \( 52,560 \text{ kWh} × ₱12 = ₱630,720 \) ### **Option B** - Annual cost: \( 35,040 \text{ kWh} × ₱12 = ₱420,480 \) --- ## **Step 3: Calculate Total 12-Year Cost** ### **Option A: Standard Escalator** - **Purchase Cost:** ₱4,000,000 - **12-year Maintenance Cost:** ₱200,000 × 12 = ₱2,400,000 - **12-year Energy Cost:** ₱630,720 × 12 = ₱7,568,640 - **Total 12-Year Cost:** ₱4,000,000 + ₱2,400,000 + ₱7,568,640 = **₱13,968,640** --- ### **Option B: High-Efficiency Escalator** - **Purchase Cost:** ₱6,000,000 - **12-year Maintenance Cost:** ₱250,000 × 12 = ₱3,000,000 - **12-year Energy Cost:** ₱420,480 × 12 = ₱5,045,760 - **Total 12-Year Cost:** ₱6,000,000 + ₱3,000,000 + ₱5,045,760 = **₱14,045,760** --- ## **Step 4: Evaluate Capacity** - **Option A:** 7,000 persons/day - **Option B:** 10,000 persons/day Option B can handle significantly more passengers daily; this matters if the mall expects heavy foot traffic. --- ## **Final Summary and Recommendation** ### **Cost Comparison Over 12 Years** - **Option A (Standard):** ₱13,968,640 - **Option B (High-Efficiency):** ₱14,045,760 ### **Conclusion** - **Option A** is slightly cheaper over 12 years (by ₱77,120). - **Option B** consumes less energy and supports more passengers, which can be vital for high-traffic malls. **Recommendation:** - If the mall's daily passenger volume does not exceed 7,000, **Option A** is the most cost-effective. - If higher capacity is required or future growth is expected, **Option B** may be justified despite the marginally higher total cost. **Final Decision:** Choose **Option A** for lowest total 12-year cost, unless higher capacity is needed for mall operations.

# Step-by-Step Summary ## **Step 1: Calculate Annual Energy Consumption** Calculate the annual operating hours for both escalator options. Determine the annual energy consumption based on their kilowatt-hour usage. ## **Step 2: Calculate Annual Energy Cost** Multiply the annual energy consumption by the electricity rate. This provides the annual cost of energy for each escalator option. ## **Step 3: Calculate Total 12-Year Cost** Sum the purchase cost, maintenance cost, and energy cost over 12 years for both escalators. This gives a comprehensive view of the total costs associated with each option. ## **Step 4: Evaluate Capacity** Assess the passenger capacity for each escalator option. Option B supports a higher daily passenger volume, which may be relevant for the mall's operations. ## **Final Summary and Recommendation** Option A has a lower total cost over 12 years compared to Option B. However, if higher capacity is essential for the mall, Option B may be more suitable despite its higher cost.