Question

You work at a toy company. You talk to the accounting department and figure out that the fixed operating cost is roughly $50,000 a month. As an engineer, you also calculate that it cost roughly $40 per unit of output. You then notice that due to supply and demand that the selling price per unit is about p = $200-1.6D. Determine the optimal volume for this product and what are the breakeven point(s)?

Answer 1

Solution:-

Given that

Here, the profit function of the firm is given by:

Profit(π) = Price(P) * Quantity(D) - Variable Cost(40*D) - Fixed Cost

π = P*D - 40D - 50,000

π = (200-1.6D)D - 40D -50,000

π = (160 - 1.6D)D -50,000

To maximise profit, we differentiate the profit function wrt D and equate it to zero.

dπ/dD = (160 - 1.6D) + D(-1.6) = 0

Therefore,

160 -3.2D = 0

3.2D = 160

D = 160/3.2

D = 50

Hence producing a volume of D = 50 units should be produced to maximise the profit.

Hence π = (160 -1.6*50)*50 - 50000 = -46000

The breakeven point is determined by equating Total Revenue to Total Costs.

Hence P*D = 40D + 50,000

Hence (200-1.6D)D = 40D +50,000

160D - 1.6D^2 - 50,000 = 0

Solving this quadratic equation, we get D as a complex number and not a real number. Hence the breakeven point doesn't exist.

We can validate this by using the previous part. Since the maximum profit can't reach zero, there exists no breakeven point.

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