A company produces 500 units of a product per day at a cost of $8 per unit. They sell each unit for $12. After 7 days, they reduce production by 20% but cut cost per unit by 15%. What is the profit for the next 5 days? - Parker Core Knowledge
Title: Analyzing Profit for a Manufacturing Company: From Full Capacity to Reduced Production and Cost Savings
Title: Analyzing Profit for a Manufacturing Company: From Full Capacity to Reduced Production and Cost Savings
Meta Description:
This article explores the profit dynamics of a company producing 500 units daily at $8 per unit, selling each for $12. After 7 days, production drops by 20% and unit costs fall by 15%. We calculate the profit for the next 5 days under revised operations.
Understanding the Context
Introduction
Understanding profit performance is essential for any manufacturing business, especially when production volume and unit costs fluctuate. In this scenario, a company starts producing 500 units per day at $8 per unit, selling each unit for $12—yielding strong margins. After 7 days, production cuts by 20%, and unit costs decrease by 15%, changing the profit equation. This article examines revenue and costs under these new conditions to calculate the profit for the following 5 days.
Initial Phase: 7 Days of Full Production
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Key Insights
Production:
- 500 units/day
- Cost per unit: $8
- Selling price: $12
- Daily revenue = 500 × $12 = $6,000
- Daily variable cost = 500 × $8 = $4,000
- Daily gross profit = $6,000 – $4,000 = $2,000
Total profit after 7 days:
$2,000 × 7 = $14,000
After 7 Days: Reduced Production and Lower Costs
Changes:
- Production reduced by 20%:
New daily production = 500 × (1 – 0.20) = 400 units/day - Cost per unit reduced by 15%:
New cost per unit = $8 × (1 – 0.15) = $6.80
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Daily Metrics for Next 5 Days
- Units produced per day: 400
- Cost per unit: $6.80
- Selling price: $12
Daily calculations:
Revenue:
$12 × 400 = $4,800
Variable Cost:
$6.80 × 400 = $2,720
Gross Profit per Day:
$4,800 – $2,720 = $2,080
Total Profit Over Next 5 Days
Since daily gross profit remains consistent:
$2,080 × 5 = $10,400
