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Funtime Quadcopters plans to sell a standard quadcopter ​(toy drone) for $ 55 and a deluxe quadcopter for $ 85. Funtime purchases the standard quadcopter for $ 45 and the deluxe quadcopter for $ 65. Management expects to sell two deluxe quadcopters for every three standard quadcopters. The​ company's monthly fixed expenses are $ 11 comma 900. How many of each type of quadcopter must Funtime sell monthly to​ breakeven? To earn $ 7 comma 700​?

Respuesta :

Edufirst

Answer:

  • Funtime must sell 510 standard quadcopters and 340 deluxe quadcopters every month to breakeven.

  • Funtime must sell 840 standard quadcopters and 560 deluxe quadcopters to earn $ 7,700 monthly.

Explanation:

A. To breakeven, the revenue must equal the total costs.

1. Write the expresssion of revenue

Revenue = price × number of units

Revenue from standard quadcopter

    Naming s the number of standard quadcopters sold:

  • $55 × s = 55s

Revenue from deluxe quadcopter

    Naming d the number of deluxe quadcopters sold:

  • $85 × d = 85d

Total revevue:

  • 55s + 85d

2. Write the expression of cost

Purchase price of standard quadcopters

  • $45s

Purchase price of deluxe quadcopters

  • $65d

Fixed  monthly expenses

  • $11,900

Total cost:

  • 45s + 65d + 11,900

3. Relation between number of deluxe quadcopters and standard quadcopters

Two deluxe quadcopters for every three standard quadcopters

  • d = (2/3)s

4. Substitute d with (2/3)s in the expressions, writhe the equation and solve

Revenue = 55s + 85(2/3)s

Cost = 45s + 65(2/3)s + 11,900

Revenue = Cost

  • 55s + 85(2/3)s - 45s - 65(2/3)s - 11,900 = 0

Multiply the equation by 3, to eliminate the denominators:

  • 165s + 170s - 135s - 130s - 35,700 = 0

Add like terms and add 35,700 to both sides

  • 70s = 35,700

Divide by 70

  • s = 510

Substitue s in d = (2/3)s

  • d = (2/3)510 = 340.

Therefore, Funtime must sell 510 standard quadcopters and 340 deluxe quadcopters every month to breakeven.

B. To earn $7,700

Profit = revenue - cost

  • 7,700 = 55s + 85(2/3)s - 45s - 65(2/3)s - 11,900

Add 11,900 to both sides

  • 19,600 = 55s + 85(2/3)s - 45s - 65(2/3)s

Mutliply the equation by 3:

  • 58,800 = 165s + 170s - 135s - 130s

Do the operations:

  • 58,800 = 70s

  • s = 58,800 / 70 = 840

d = (2/3)840 = 560

Hence, Funtime must sell 840 standard quadcopters and 560 deluxe quadcopters to earn $ 7,700 monthly.

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