Scenario: Business Planning - Learn to solve complex problems that require multiple mathematical concepts!
You're starting a small business selling handmade crafts. You need to plan your first month of operations. Here are the details: You can make 15 items per day, each item costs $8 to make, and you sell them for $18 each. You work 20 days per month. Your monthly expenses are: rent $500, utilities $150, and materials $1,200.
Business Challenge:
Calculate your monthly profit and determine if you need to adjust your pricing or production to break even.
Production:
Monthly Expenses:
Problem Solving Steps:
Items per day × Working days per month = Total production
15 × 20 = 300 items per month
Total items × Selling price per item = Total revenue
300 × $18 = $5,400
Total items × Cost per item = Production costs
300 × $8 = $2,400
Rent + Utilities + Materials = Total expenses
$500 + $150 + $1,200 = $1,850
Production costs + Monthly expenses = Total costs
$2,400 + $1,850 = $4,250
Total revenue - Total costs = Monthly profit
$5,400 - $4,250 = $1,150
Good News: Your business is profitable! You're making $1,150 per month.
Profit Margin: $1,150 ÷ $5,400 = 21.3%
Break-even Point: You need to sell at least 236 items to break even
Recommendation: Your current pricing and production levels are working well!
A restaurant serves 120 customers per day at an average of $25 per customer. Daily costs are: food $800, labor $600, rent $200. Calculate the daily profit and monthly profit (30 days).
Your solution:
You're organizing a school dance. Tickets cost $15 each. You expect 200 students. Costs are: venue $800, DJ $300, decorations $200, refreshments $400. How much profit will you make, and what's the minimum number of tickets needed to break even?
Your analysis: