1°. A manufacturer sells its product at $15.00 per unit. Your estimated fixed costs at $12,000.00 and variable costs at 40% of the total income. Your Average production capacity is 6,000 units/month. Determine: A) The recipe function B) The total cost function; C) The total profit function: D) The breaking point E) What is the profit made in the production and sale of your average capacity?

Given information: Selling price per unit (P) = $15.00 Fixed costs (FC) = $12,000.00 Variable costs (VC) = 40% of total income (revenue) Average production capacity (Q) = 6,000 units/month A) The revenue function (R) can be calculated as: R = P * Q R = $15.00 * Q B) The total cost function (TC) is the sum of fixed costs and variable costs. Variable costs are calculated as a percentage of revenue (income): VC = 40% of R VC = 0.40 * R TC = FC + VC TC = $12,000.00 + 0.40 * R C) The total profit function (π) is calculated as the difference between revenue and total cost: π = R - TC π = R - ($12,000.00 + 0.40 * R) D) The breakeven point is the level of production at which total revenue equals total cost, resulting in zero profit. To find the breakeven point, set the profit function equal to zero and solve for Q: π = 0 $15.00 * Q - ($12,000.00 + 0.40 * ($15.00 * Q)) = 0 Solve for Q: $15.00 * Q - ($12,000.00 + 0.60 * Q) = 0 $15.00 * Q - $12,000.00 - 0.60 * Q = 0 $15.00 * Q - $0.60 * Q = $12,000.00 $14.40 * Q = $12,000.00 Now, solve for Q: Q = $12,000.00 / $14.40 Q = 833.33 (approximately) So, the breakeven point is approximately 833 units. E) To find the profit made in the production and sale of your average capacity (6,000 units/month), substitute Q = 6,000 into the profit function: π = $15.00 * 6,000 - ($12,000.00 + 0.40 * ($15.00 * 6,000)) Now, calculate π: π = $90,000.00 - ($12,000.00 + $36,000.00) π = $90,000.00 - $48,000.00 π = $42,000.00 So, the profit made in the production and sale of your average capacity is $42,000.00.