1. (1st degree function) a company has a fixed cost of $2359.00 in one month. The production price value per unit is $12.80 per piece. The retail price for each piece is $15.50. Find the Total Cost, Revenue and Profit functions and answer: a) The total cost for 1000 pieces produced in a month b) The revenue when 2154 pieces are sold c) How many pieces are sold so that the profit is zero?

To find the Total Cost (C), Revenue (R), and Profit (P) functions, you can use the following information: Fixed Cost (FC) = $2359.00 Production Price per Unit (PPU) = $12.80 Retail Price per Unit (RPU) = $15.50 a) Total Cost for 1000 pieces produced in a month: Total Cost (C) is the sum of the fixed cost and the variable cost, which is the production cost per unit multiplied by the number of units produced: C(x) = FC + (PPU * x) Where x is the number of pieces produced. C(1000) = $2359 + ($12.80 * 1000) C(1000) = $2359 + $12800 C(1000) = $15159.00 So, the total cost for producing 1000 pieces in a month is $15,159.00. b) Revenue when 2154 pieces are sold: Revenue (R) is the total income from selling x pieces at the retail price per unit: R(x) = RPU * x R(2154) = $15.50 * 2154 R(2154) = $33,387.00 The revenue when 2154 pieces are sold is $33,387.00. c) To find the number of pieces sold for zero profit, we need to find the profit function and then set it equal to zero. Profit (P) is calculated as the difference between revenue and cost: P(x) = R(x) - C(x) P(x) = (RPU * x) - (FC + (PPU * x)) Now, set P(x) equal to zero and solve for x: (RPU * x) - (FC + (PPU * x)) = 0 (15.50 * x) - (2359 + (12.80 * x)) = 0 15.50x - 2359 - 12.80x = 0 2.70x = 2359 x = 2359 / 2.70 x ≈ 874.07 So, approximately 874 pieces need to be sold for the profit to be zero.