Answer:
To find the quantity for the break-even point, we need to determine the value of x at which the revenue equals the total cost.
Explanation:
The total cost consists of two components: the fixed cost and the variable cost. The variable cost is calculated by multiplying the unit cost by the quantity produced.
Given that the unit cost is $16 and the fixed cost is $16320, the total cost can be expressed as:
Total Cost = Fixed Cost + (Unit Cost * Quantity)
Total Cost = 16320 + (16 * Quantity)
The revenue function is given by R(x) = -2x^2 + 438x, where x represents the quantity of ice cream tubs produced.
To find the break-even point, we set the revenue equal to the total cost:
R(x) = Total Cost
-2x^2 + 438x = 16320 + (16 * Quantity)
Now, we need to solve this equation to find the value of x.
-2x^2 + 438x - 16x - 16320 = 0
-2x^2 + 422x - 16320 = 0
Next, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the values of x that satisfy the equation, we can determine the quantity for the break-even point.