A manufacturer of a particular item can sell all the output made by him at a selling price of ₹80 per item. The cost of materials and labor required to produce each article is ₹60 and it costs an additional ₹5,000 per week to operate the plant. How many units should he produce and sell to make a profit of at least ₹15,000 per week?

Given:

Selling price per item: ₹80
Cost of materials and labor per item: ₹60
Additional weekly operating cost: ₹5,000
Desired weekly profit: ₹15,000

Concept or Formula:

Profit is calculated as total revenue minus total costs. In this case, the total costs include per item costs and weekly operating costs.

Calculation:

Calculate the profit made per item sold.

⇒ Profit per item = Selling price per item - Cost of materials and labor per item

⇒ ₹80 - ₹60 = ₹20

Calculate the total desired profit.

⇒ Total desired profit = Desired weekly profit + Weekly operating cost

⇒ ₹15,000 + ₹5,000 = ₹20,000

Determine the number of units needed to cover the total desired profit. Round up to the next whole number since we cannot have a fraction of an item.

⇒ Number of units = Total desired profit / Profit per item

⇒ ₹20,000 / ₹20 = 1000 units

∴ The manufacturer should produce and sell at least 1000 units per week to make a profit of at least ₹15,000.