Question

A computer software manufacturer wants to start the production of floppy disks. He observes that
he will have to spend 2 lakh for the technical know-how. The cost of setting up the machine is
88,000 and the cost of producing each unit is 30. He can sell each floppy at 45. Determine
(i) the total cost function for producing x floppies, and (ii) the break-even point.

Answer 1

(i)The total cost function for producing x floppies is given by: Total Cost = 288000 + 30x and (ii) The break-even point is approximately 19200 floppy disks.

Cost components:

Technical know-how cost: ₹2,00,000

Machine setup cost: ₹88,000

Cost of producing each unit (variable cost): ₹30

(i) Total Cost Function for Producing x Floppies:

The total cost function is the sum of fixed costs and variable costs. Fixed costs do not change with the production volume, while variable costs depend on the number of units produced.

Fixed Costs:

Fixed costs include the technical know-how cost and the machine setup cost.

Total Fixed Costs = Technical know-how cost + Machine setup cost

$= 200000 + 88000= 288000$

Variable Costs:

Variable costs depend on the number of units produced. In this case, the cost of producing each unit is given as ₹30.

Total Variable Costs = Cost per unit × Number of units produced

$= 30 \times x= 30x$

Total Cost Function:

The total cost function is the sum of fixed costs and variable costs:

Total Cost = Total Fixed Costs + Total Variable Costs

$= 288000 + 30x$

(ii)Break-even Point:

The break-even point is the production level at which the total revenue equals the total cost, resulting in zero profit or loss.

The total revenue is the product of the selling price per unit and the number of units sold. The selling price per unit is given as ₹45.

Total Revenue = Selling price per unit × Number of units sold

$= 45 \times x= 45x$

At the break-even point, total revenue equals total cost:

Total Revenue = Total Cost

$45x = 288000 + 30x$

To find the break-even point, we need to solve this equation for x:

$45x - 30x = 288000\\15x = 288000\\x = 2,88,000 \div 15\\x \approx 19,200$

Therefore, the break-even point is approximately 19,200 floppy disks.

To summarize:

(i) The total cost function for producing x floppies is given by: Total Cost = 288000 + 30x

(ii) The break-even point is approximately 19200 floppy disks.

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