. A furniture company makes two products: book shelves selling for ₱5,000 and cabinets selling for ₱8,000. The direct cost per unit is ₱3,000 and ₱4,000, respectively. The company has no difficulty in selling all the products it can manufacture. The assembly department has 60 hours available per week and the finishing department can handle up to 48 hours of work per week. Manufacturing one book shelf requires 4 hours in assembly and 2 hours in finishing. Each cabinet requires 2 hours in assembly and 4 hours in finishing. How can the management allocate the limited man-hour of the two departments in a way which will secure the largest possible net return
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Formulate an LP model for the following problems.
1. A furniture company makes two products: book shelves selling for ₱5,000 and cabinets
selling for ₱8,000. The direct cost per unit is ₱3,000 and ₱4,000, respectively. The
company has no difficulty in selling all the products it can manufacture. The assembly
department has 60 hours available per week and the finishing department can handle
up to 48 hours of work per week. Manufacturing one book shelf requires 4 hours in
assembly and 2 hours in finishing. Each cabinet requires 2 hours in assembly and 4
hours in finishing. How can the management allocate the limited man-hour of the two
departments in a way which will secure the largest possible net return?
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- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.The Scottville "Mill" produces five different fabrics. Each fabric can be woven on one or more of the mill's 38 looms. The sales department has forecast demand for the next month. The demand data are shown in Table 1.0 below along with data on the selling price per yard, variable cost per yard, and purchase price per yard. The mill operates 24 hours a day and is scheduled for 30 days during the coming month. The Mill has two types of looms: dobbie and regular. The dobbie looms are more versatile and can be used for all five fabrics. The regular looms can produce only three of the fabrics. The Mill has a total of 38 looms: 8 are dobbie and 30 are regular. The rate of production for each fabric on each type of loom is given in Table 1.1. The time to change over from producing one fabric to another is negligible and does not have to be considered. The Scottsville Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at…8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. Cabinet Style Carpentry (Hours/Cabinet) Painting (Hours/Cabinet) Finishing (Hours/Cabinet) Net Revenue/Cabinet ($) French Provincial 3 1.5 0.75 28 Danish Modern 2 1 0.75 25 Department Capacity (Hours) 360 200 125 a) Formulate as an LP problem. b) Solve using an LP software program or…
- 8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. Perform the four steps (i.e., define variables, determine objective function, identify constraints, list the non-negativity statement) and write equations. Use the table in the picturePlease answer this using EXEL AND SOLVER ADD IN. Include and identify decision variables, objective, and constraints. Please also upload what the info in solver you added was!!!! It is summertime and your winter coat factory is trying to decide its production schedule and staffing level for the next season. You are forecasting demand of 5000 coats in October, 8000 coats in November, 8000 coats in December, 12000 coats in January, 12000 coats in February and 9000 coats in March. You want to manufacture these coats at the lowest cost possible during your production window (October-March). The first decision you need to make is how many people to hire. Each employee will cost $2500 a month. You don’t want to hire or fire any employees mid-season in order to minimize disruptions in your factory floor. You can have employees idle if there isn’t sufficient work for them to do. Employees still need to be paid even if they are idle. An employee works 20 business days a month and takes half a…LPM Corp. produces and sells two types of frozen burgers, Turkey Burgers and Veggie Burgers. In the most recent month, the firm sold 12,000 Turkey Burgers and 8,000 Veggie Burgers. Turkey Burgers sold for $14.00 per box and variable costs were $7.40 per box. The Veggie Burgers sold for $16.00 per box and variable costs were $8.25 per box. The fixed expenses of the entire company were $41,160. If the sales mix were to shift toward the Turkey Burgers product line with total sales volume remaining constant at 20,000, the overall break-even point for the entire company:
- Direction: Analyze the given problem and show your complete solution. The GEM maker of jewelry makes two bracelet designs, heart design and flower design. The bracelets are made of gold and platinum. The store has 28 ounces of gold and 20 ounces of platinum. Each heart design bracelet requires 3 ounces of gold and 2.5 ounces of platinum and makes a profit of P2500, while each flower design bracelet requires 4.5 ounces of gold and 3 ounces of platinum and makes a profit of P3400. How many heart design bracelets and flower design bracelets should be produced to maximize the profit? Decision variables Tabulation Objective function and constraints Graph and solution Optimum solution DecisionGarfield Industries is expanding its operations throughout the Southeast United States. Garfield anticipates that the expansion will increase sales by $1,000,000 and increase operating costs (excluding depreciation and amortization) by $700,000. Depreciation and amortization expenses will rise by $50,000, interest expense will increase by $150,000, and the company’s tax rate will remain at 40 percent. If the company’s forecast is correct, how much will net income increase or decrease, as a result of the expansion?UST 40,000 (Commerce 5,000; Medicine 15%; AB 20%; Law 5% and others)Average price per computer device Php25,000Average price per Apple device Php30,000In UST, students from Commerce, Law, and AB purchased at least one (1) computer device inDecember 2020.What is the market penetration of computer devices in individual colleges?Given that students replace their computer devices once every 2 years on average, what is theprojected market size (units/revenues) for computer devices for these colleges until the end of2025?What is the concentration of sales/revenue of computer devices among the colleges (CDI)?
- A wood products firm uses available time at the end of each week to make goods for stock.Currently, two products on the list of items are produced for stock: a chopping board and a knifeholder. Both items require three operations: cutting, gluing, and finishing. The manager of thefirm has collected the following data on these products.TIME PER UNIT (MINUTES)Item Profit/Unit Cutting Gluing FinishingChopping board $2 1.4 5 12Knife holder $6 0.8 13 3The manager has also determined that, during each week, 56 minutes are available for cutting, 650minutes are available for gluing, and 360 minutes are available for finishing.a. Determine the optimal quantities of the decision variables if the goal is to maximize profit.b. Which resources are not completely used by your solution? How much of each resource isunused?The ABC Company is making a production plan for the next year, given the sales forecast for the next year as: Quarter 1 2 3 4 Total Sales Forecast (units) 9,000 12,000 16,000 12,000 49,000 Currently, the firm has 12 employees, each producing up to 1,000 units per quarter and earning $2,000 per quarter. The firm estimates its inventory carrying cost to be $2 per unit of ending inventory per quarter and its hiring or layoff costs to be $1,600 per employee. The company currently has an inventory of 2,000 units and wishes to have an ending inventory of at least 1,000 units at the end of each quarter. The company does not plan to incur inventory shortages. Find the optimal production plan that minimizes the total cost by Excel solverLake Stevens Marina has estimated that fixed costs per month are $350,000 and variable cost per dollar of sales is $0.30 . The selling price per dollar of sales is: $1.00 Determine the effect on the break-even point in sales dollars considering each of the following independently. 1. Total fixed costs increase to $365,000. Break-even point = ÷ = 2. Variable costs decline to $0.25 per sales dollar. Break-even point = ÷ = 3. The anticipated sales volume increases to $1,100,000. Break-even point = ÷ = Comment on the BEPs from the above analyses in questions 1,2,3.