XYZ company can manufacture their own products and sells them. They are able to control the demand by changing the price that is determined by the equation below. The company is thinking of maximizing their profit. The fixed cost is $1,000 per month and the variable cost is $40 per unit. Find the number of units that must be manufactured and sold monthly to maximize profit. (Demand D in the equation is monthly) Hint: Profit = Total Revenue - Total Cost 2,700 5,000 p = $38+ D for D > 1 D2
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- A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…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.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?
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