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?

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:

Revenue from deluxe quadcopter

    Naming d the number of deluxe quadcopters sold:

Total revevue:

2. Write the expression of cost

Purchase price of standard quadcopters

Purchase price of deluxe quadcopters

Fixed  monthly expenses

Total cost:

3. Relation between number of deluxe quadcopters and standard quadcopters

Two deluxe quadcopters for every three standard quadcopters

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

Multiply the equation by 3, to eliminate the denominators:

Add like terms and add 35,700 to both sides

Divide by 70

Substitue s in d = (2/3)s

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

B. To earn $7,700

Profit = revenue - cost

Add 11,900 to both sides

Mutliply the equation by 3:

Do the operations:

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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