Profit and Cost Functions Analysis

The video tutorial explains how to calculate the profit function for a company producing ice cream tubs, given the unit and fixed costs, and the revenue function. It demonstrates deriving the profit function by subtracting the cost function from the revenue function. The tutorial then shows how to find the smallest break-even point by setting the profit function to zero and solving the resulting quadratic equation. Finally, it verifies the solutions graphically by plotting the revenue, cost, and profit functions, confirming the break-even points.

What is the unit cost to produce a tub of ice cream?

• $10

• $13

• $15

• $20

What is the fixed cost mentioned in the problem?

• $10,000

• $14,580

• $12,000

• $16,000

How is the cost function C(x) expressed?

• C(x) = 13x - 14,580

• C(x) = 14,580x + 13

• C(x) = 14,580 - 13x

• C(x) = 13x + 14,580

What is the formula for the profit function P(x)?

• P(x) = R(x) - C(x)

• P(x) = R(x) * C(x)

• P(x) = R(x) + C(x)

• P(x) = C(x) - R(x)

What is the quadratic term in the profit function?

• -2x^2

• 2x^2

• -x^2

• x^2

What is the smallest break-even point in terms of quantity?

• 54 tubs

• 100 tubs

• 200 tubs

• 135 tubs

Which method is used to solve for the break-even point?

• Linear equation

• Quadratic formula

• Graphical method

• Trial and error

What is the value of the discriminant used in the quadratic formula?

• 189

• 7290

• 6561

• 81

How can the break-even point be verified graphically?

• By plotting the profit function only

• By plotting both revenue and cost functions

• By plotting only the revenue function

• By plotting only the cost function

What are the x-intercepts of the profit function graph?

• 60 and 140

• 50 and 130

• 54 and 135

• 70 and 150