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- The accountant of Royal Products provided the following information for purposes of determining the optimal product mix: Product King (K) Product Queen (Q) Marginal income per unit R30 R36Machine hours required per unit 6 6Marginal income per machine hour R5 R6Ranking in terms of machine hours 2nd 1stLabour hours required per unit 3 6Marginal income per labour hour R10 R6Ranking in terms of labour hours 1st 2ndAnnual demand for product in units 12 000 15 000Labour hours available per annum 65 000 Machine hours available per annum 82 000 Required: Determine the optimal product mix by means of the application of linear programming techniques. (Hint: Start with your objective function and all necessary constraints.)A manufacturing firm has four factories from which product is shipped to three warehouse for onward distribution to stores. The following table reports a partial shipment plan to meet demand. The partial shipment plan, the total supplies at the factories and the required demands at the warehouses are reported in the table below. Factory Warehouse A Warehouse B Warehouse C Supply Factory 1 70 210 100 380 Factory 2 110 90 Answer 278 Factory 3 200 110 220 530 Factory 4 120 90 80 290 Demand 500 500 478 For the above shipment plan to be feasible, what is the number of units shipped from Factory 2 to Warehouse C? Report the number within the table.A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.
- Terra Mesa Manufacturing uses a job order cost system to account for its production of specialty patio furniture. At the beginning of June, Terra Mesa had one job in Work in Process, job A75. Management has chosen direct labor cost as its activity base. The costs incurred to date on job A75 are as follows: Direct materials $8260 Direct labor 10500 Overhead 13125 During June, Terra Mesa added the following costs for direct materials and direct labor to job A75: Direct materials $2630 Direct labor 4620 Job A75 was competed on June 30. What is the cost of job A75? $26010 $39135 $44910 $42831The Lechería La Vaquita company currently has three-star products, but it faces a problem of capacity to satisfy the demand for these products. In total, it has 65,000 machine hours per month for the production of these three products. The production time to produce a batch of 1000 liters each product, as well as its monthly demands are shown in the following table: * TABLE * Because in recent months there have been advertising campaigns for Leche Choco-Chavo and Leche Chavo Light, the company wants the demands for these products to be the first to be satisfied with the same level of importance, while Leche Chavo as it is a product already well positioned, it is the third priority of these products. Formulate the goal programming mathematical model for this problem by clearly defining the sets, constraint variables, parameters, objective function (s), and constraints.Determine the set of prices that would satisfy the condition of each the three markets using Gauss-Jordan method. Given following below in the picture.
- Suppose that the manager in Example 1 wants to establish an optimal inventory policy for frozen orange juice. Again, it is estimated that a total of 1200 cases will be sold at a steady rate during the next year. The manager plans to place several orders of the same size spaced equally throughout the year. Use the following data to determine the economic order quantity; that is, the order size that minimizes the total ordering and carrying cost.1. The ordering cost for each delivery is $75. 2. It costs $8 to carry one case of orange juice in inventory for 1 year. (Carrying costs should be computed on the average inventory during the period.)Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage(hours) AnnualMaintenance Expense 19 24 16 29 26 37 34 44 38 54 23 38 30 40 37 46 46 59 44 47 -select your answer choices- b. p-value less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Conclusion Do not conclude that there is a significant relationship between expense and weekly usage Conclude that there is a significant relationship between expense and weekly usage d. No, the expected maintenance expense is less than $3000 Yes, the expected maintenance expense is greater than $3000The company has data on demand and factory capacity for the next 4 months as in the table. Unit cost with regular time $ 24, overtime cost $ 28, on subcontract $ 34. Storage costs $ 2 per unit per month; backorders cost $ 5 per unit per month. Initial inventory is as many as 120 units, and it is expected that by the end of July there will be an inventory of 100 units. April May June July Demand 460 450 480 480 Regular Capacity 370 370 380 380 Overtime Capacity 60 60 60 60 Subcontract Capacity 30 30 30 30 Use the transportation method to optimize the aggregate plan. Determine the production cost each month and the total cost for 4 months
- The Arctic Air Company produces residential air conditioners. The manufacturing manager wants to develop a sales and operations plan for the next year based on the following demand and capacity data (in hundreds of product units): Undertime is unpaid, and no cost is associated with unused overtime or subcontractor capacity. Producing one air conditioning unit on regular time costs $1,000, including $300 for labor. Producing a unit on overtime costs $1,150. A subcontractor can produce a unit to Arctic Air specifications for $1,250. Holding an air conditioner in stock costs $60 for each 2-month period, and 200 air conditioners are currently in stock. The plan calls for 400 units to be in stock at the end of period 6. No backorders are allowed. Use the transportation method to develop a plan that minimizes costs.A supermarket expects to sell 16,000 boxes of sugar in a year. Each box costs $2, and there is a fixed delivery charge of $20 per order. If it costs $1 to store a box for a year, what is the order size and how many times a year should the orders be placed to minimize inventory costs?A shoe company forecasts the following demands during the next six months: month 1 – 200; month 2 – 260; month 3 – 240; month 4 – 340; month 5 – 190; month 6 – 150. It costs $7 to produce a pair of shoes with regular-time labor and $11 with overtime labor. During each month, regular production is limited to 200 pairs of shoes, and overtime production is limited to 100 pairs. It costs $1 per month to hold a pair of shoes in inventory. The initial inventory is 0. Let xi = pairs of shoes produced in month i using regular-time labor, yi = pairs of shoes produced in month i using overtime labor, and zi = inventory of shoes at the end of month i. Using these decision variables, formulate an LP that minimizes the total cost and meets the demand on time in the next six months.