Question

the following information pertains to supersupper's 2020 operations: selling price per unit $50 variable costs per unit $10 total fixed costs $55,000 the sales dollars required to obtain a target pretax profit of $17,000 is:

Answer 1

The required volume sales in order to fulfill a target after-tax profit of $17,000 is 1788 units.

Given,

x = number of units sold.

Revenue function:

R(x) = selling price per unit × number of units sold.

R(x) = 50.x

Cost function:

C(x) = variable cost + fixed cost

      = variable costs per unit × number of units sold + fixed cost

      = 10.x + 50,000

Gross profit function:

P(x) = R(x) - C(x)

P(x) = 50x - (10.x + 50,000)

P(x) = 40x - 50,000

Net profit = (1 - tax rate) × Gross profit

NP (x) = (1 - 0.21) × (40x - 50,000)

NP(x) = 0.79 × (40x - 50,000)

NP(x) = 31.6x - 39500

17,000 = 31.6x - 39,500

31.6x = 56,500

x = 1787.97 = 1788

Hence, the company needs to sell 1788 units to fulfill the target

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