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 1 Add file
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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?
- PUP 48,213 UST 40,000 FEU 27,889 LRT2 200,000 passengers daily If 60% of PUP, 30% of UST, and 85% of FEU students take LRT2 daily and pays an average fare of Php25 per day… What is the total annual market size (revenue) of LRT2? What is the total annual market size (revenue) of the 3 schools? If operations is halted for 1 week, what is the projected loss in revenues? What is the market share (volume) of: PUP students? UST students? Feu students?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?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
- Please show solution for this question. Determine the revenue (R) and cost (TC). The production will vary according to the sales volume. Express the equation as follows. R = 100N – 0.001N2 TC = 0.005N2+4N+60,000 Find 1) The most profitable production volume. 2) Volume of production at break even point. 3) Production volume with lowest average cost. Answer 1) 8,000 units 2) 6,000 units 3) 3,464 unitsHau Lee Furniture, Inc., spends 60% of its sales dollars in the supply chain and has a current gross profit of $10,000. Hau wishes to increase gross profit by $5,000 (50%). He would like to compare two strategies: reducing material costs vs. increasing sales. The current material costs and production costs are 60% and 20%, respectively, of sales dollars, with fixed cost at a constant $10,000. Analysis indicates that an improvement in the supply chain that would reduce material costs by 8.3% ($5,000/$60,000) would produce a 50% net profit gain for Hau, whereas a much larger 25% increase in sales ($25,000/$100,000) would be required to produce the same result. Now Hau finds its current profit of $10,000 inadequate. The bank is insisting on an improved profit picture prior to approval of a loan for some new equipment. Hau would like to improve the profit line to $25,000 so he can obtain the bank’s approval for the loanWhat percentage improvement is needed in the supply chain strategy for…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 complete solution.
- 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.Jenni has decided to start knitting during quarantine. She decides to open an etsy shop where she can sellknitted hats. Each hat costs $4.50 in materials to produce, in addition to the fee of $150 to license her shop.She plans on selling each hat for $24.50. (a) Write the cost, revenue, and profit equations for Jenni’s hat buisness. (b) Determine the profit if 13 hats are sold.(c) Determine thebreak-evenpoint.A company estimated that the relationship between the unit price and demand per month for a potential new product is approximated by P = $ 100 – $ 0.1D. The company can produce the product by increasing fixed costs $ 17,500 per month, and the estimated variable costs is $ 40 per unit. What is the optimal demand, D*, and based on this demand, should the company produce new product? Why? a) Work out the complete solution by differential calculus, starting with formula for profit or loss per month b) Solve graphically for an approximate answer