The monthly demand is now 20,000 - 5p and the variable (or marginal) cost equals 1,000, while the fixed costs equal one million (per month). Determine the optimal price and subsequent monthly sales quantity and profits.
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- A company is negotiating a contract to sell wooden boards overseas. The fixed cost that canbe allocated to the production of boards is $800,000 per month. The variable cost perthousand board feet is $155.50. The price charged will be determined byp = $600 − (0.5)D per 1,000 board feet.(i) For this situation, determine the optimal monthly sales volume for this product andcalculate the profit (or loss) at the optimal volume.(ii) Calculate/Identify the range of profitable demand during a month.A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. 1) What is the company’s range of profitable output per year?A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month.a) Derive how to find the number of units that should be produced annually to maximize profit.b) What is the maximum profit per year?c) What is the annual breakeven point?d)What is the company’s range of profitable output per year?
- 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?Short Grass Incorporated is a distributor of golf balls. Martin's Golf Supplies is a local retail outlet which sells golf balls. Martin's purchases the golf balls from Short Grass Incorporated at $1.15 per ball; the golf balls are shipped in cartons of 72. Short Grass Incorporated pays all incoming freight, and Martin's Golf Supplies does not inspect the balls due to Short Grass' reputation for high quality. Annual demand is 159,520 golf balls at a rate of 3,691 balls per week. Martin's Golf Supplies earns 10% on its cash investments. The purchaseminus−order lead time is one week. The following cost data are available: Relevant ordering costs per purchase order $132.00 Carrying costs per carton per year: Relevant insurance, materials handling, $0.87 breakage, etc., per year What is the economic order quantity? (Round costs to the nearest cent and quantities to the nearest whole number.)The durax tire company recaps tires. The weekly fixed cost is $2500 and the variable cost per tire is $9. Price is related to demand, according to the following linear equation: V = 200 - 4.75p Develop the nonlinear profit function for the tire company and determine the optimal price, the optimal value, and the maximum profit per week.
- Pravjot Limited is launching a new product in 12 weeks and has a project team working on pricing strategy. The team has conducted some initial market research and considers that at a price of £400 no items will be sold, however for each successive price reduction of £25, weekly sales will increase by 10 units. The weekly product specific fixed costs are £2,500 and the variable costs are £75. Required: Calculate the optimum selling price and the quantity that would be sold at that price.Problem 6Cannes Croissants (not a real company) wishes to determine the optimum production quantity for its topselling product, almond croissants. The annual demandfor almond croissants is 12,000 units. The setup costs fora production run of the croissants is US$15. The holdingcost per unit per year is US$0.50. Production is mostefficient when 80 croissants are produced per day. Thecompany operates 300 days during a year.a What is the economic production quantity (EPQ)?b How many production runs will there by per year?c What is the maximum inventory level?d What is the total annual cost (in US dollars)?e What is the length of a production run in days?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.
- Suppose we know that p=1,056– D/5, where p = price in dollars and D = annual demand. The total cost per year can be approximated by $1,000 + 2D2 . a.Determine the value of D that maximizes profit. b.Show that in part(a) profit has been maximized rather than minimized. c. Find the maximum profit Show handwritten solutions.1. XYZ company’s marketing department recommends to manufacture and market a newe co-friendly and sustainable product. The financial department provides the following cost Php 6,000 is the estimated fixed costs and the estimated variable cost is Php 100 per unit. The revenue function is given with an equation of 150x - 0.005x2. Determine the following: a) the optimal demand and value (Php) b)The demand in unit and amount (Php) that will give highest revenue c) Break even points and range of profitabilityUnder a marginal cost pricing option, the market price and quantity of gizmos would be: A. $64 and 15 units B. $99 and 75 units C. $43 and 230 units D. $54 and 230 units