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- The profit (in dollars) from the sale of x lawn mowers is P(x)= 20x - 0.02x^2 - 650 (A) Find the average profit per mower if 60 mowers are produced (B) Find the marginal average profit at production level of 60 mowers, and interpret results (C)Use the results from parts A and B to estimate the average profit per mower if 61 mowers are produced ((1) The revenue for a product is R(x) = −0.004x2 + 21x − 6200 and the cost is C(x) = 0.02x + 38, for x units produced and sold.(a) Find the marginal profit for 2800 units.(b) Should output be increased or decreased to generate a higher profit?Suppose a company has fixed costs of $600 and variable costs per unit of x + 1130 dollars, where x is the total number of units produced. Suppose further that the selling price of its ²x product is 1200 - 1x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = 10,60 (b) Find the maximum revenue. $ 2880000 (c) Form the profit function P(x) from the cost and revenue functions. P(x) = 1200x - 31²) - (600 + 1² +1130x) Find the maximum profit. $ 625 (d) What price will maximize the profit? (Round your answer to the nearest cent.) $ 35 X
- A company has determined that the price and the monthly demand of one of its products are related by the equation D = √(400 − p), where p is the price per unit in dollars and D is the monthly demand. The associated fixed costs are $1,125/month, and the variable costs are $100/unit. Use this information to answer What is the optimal number of units that should be produced and sold each month? (a) 10 units (b) 15 units (c) 20 units (d) 25 units. Select the closest answer.A company sells one of its products for $10.40 per unit. Its fixed costs are $1,560 per month, and the variable cost per unit is $3.90. (a) The break-even volume is the next whole number of units.) units per month. (If necessary, round up to (b) If the selling price decreases by $2.90, the new break-even volume will be units per month. (If necessary, round up to the next whole number of units.)If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00 and its fixed cost are the same as for company A . (i) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, Π(x) for company A. (iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes. (vi) From your graph, determine the break-even level of output for company A. (vii) Derive the total revenue function, R(x) for company B. (viii) Derive the profit…
- The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x) = 2500 + 60x R(x) = 800x - x? a) Determine the maximum profit of the company. The maximum profit of the company is b) Determine the number of items that must be produced and sold to obtain the maximum profit. The number of items that must be produced and sold to obtain the maximum profit isSelling price per large Snowie $ 5.00 Ice per Snowie $ 0.20 Spoon straw (need one per Snowie) $ 0.02 Styrofoam cup (need one per Snowie) $ 0.08 Napkin (need two per Snowie) $ 0.02 Servings per gallon of syrup 28 Cost per gallon of syrup (includes concentrate, preservative, and sugar) $ 8.00 Hourly rate for workers $ 10.00 Event registration fee per day $ 25.00 Electricity, insurance, maintenance, and permit costs per month $ 250.00 Kiosk rental cost per month $ 650.00 Purchase cost of two ice shavers (5-year life) $ 3,180.00 Purchase cost of a flavor station (5-year life) $ 1,080.00 a. Number of days you anticipate opening the kiosk per month 20 b. Number of hours you will work (no wages required) per day 6…A manufacturer produces three products A, B and C which he sells in two markets. Annual sales volumes are indicated as follows: Market Products A I 4,000 18,000 20,000 II 12,000 5,000 3,000 (i) Find the total revenue in each market if sales price of A, B and C are 1.25 respectively. (ii) Also find the gross profit given the unit cost for A, B and C to be 0.80 respectively. 2, 1.50 and 1.80, 1.00 and
- A small company manufactures a certain product. Variable costs are $20 per unit and fixed costs are $10,875. The price demand relationship for this product is P = -0.25D + 250, where P is the unit sales price of the product and D is the annual demand. Total cost = fixed cost + Variable cost, TC = CF + CV Revenue = Demand x Price, TR = D x P Profit = Total Revenue – Total Cost, P = TR – TC a) Develop the equations for the total cost and total revenue. b) Find the breakeven quantity c) How many units must be sold to maximize profit? d) What is the company’s maximum profit?A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 75 – 0.1D units (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. Solve, a. What is the maximum profit per month related to thisproduct? b. What is the range of profitable demand during a month?Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level.