Question: In the initial tableau, what is the entering and leaving variable?
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A farmer has 40 acres of land on which he plans to grow coffee, mango, and coconut. Each acre of coffee requires 10 hours of labor and P3,000 of capital, each acre of mango requires 16 hours of labor and P2,000 of capital, and each acre of coconut requires 18 hours of labor and P3,000 of capital. The farmer has at most 600 hours of labor and P120,000 of capital available. If the profit from an acre of coffee is P6,000, an acre of mango is P4,000, and from an acre of coconut is P5,000, how many acres of each crop should he plant to maximize his profit?
*(Let x be the number of acres to be planted with coffee, y the number of acres to be planted with mango, z the number of acres to be planted with coconut, and P the profit) *
Question: In the initial tableau, what is the entering and leaving variable?
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.Assuming your company is producing Apple and Samsung phone cases. It is required to process in the assembly and paint shops to make either phone case. It takes 1/60 of a day and 1/40 of a day to paint an Apple case and a Samsung case in the paint shop, respectively. It takes 1/50 of a day to assemble either type of case in the assembly shop. An Apple phone case and a Samsung phone case yield profits of $300 and $220, respectively, per case sold. What is a maximum-profit daily production plan for your company?
- A Las Vegas, Nevada, manufacturer has the option to make or buy one of its component parts. The annual requirement is 20,000 units. A supplier is able to supply the parts for $10 per piece. The firm estimates that it costs $600 to prepare the contract with the supplier. To make the parts in-house, the firm must invest $50,000 in capital equipment, and the firm estimates that it costs $8 per piece to make the parts in-house. Assuming that cost is the only criterion, use breakeven analysis to determine whether the firm should make or buy the item. 1. What is the breakeven quantity? 2. Should the manufacturer Make or Buy? 3. What is the cost savings using your decision in number 2 (above)? Show the total cost for each scenario then the savings amount.A young computer engineer has $12,000 to invest and three different investment options (funds) to choose from. Type 1 guaranteed investment funds offer an expected rate of return of 7%, Type 2 mixed funds (part is guaranteed capital) have an expected rate of return of 8%, while an investment on the Stock Exchange involves an expected rate of return of 12%, but without guaranteed investment capital. Computer engineer has decided not to invest more than $2,000 on the Stock Exchange in order to minimize the risk. Moreover for tax reasons, she needs to invest at least three times more in guaranteed investment funds than in mixed funds. Assume that at the end of the year the returns are those expected; she is trying to determine the optimum investment amounts. (a) Express this problem as a linear programming model with two decision variables.(b) Solve the problem with the graphical solution procedure and define the optimum solution.Barbara Flynn sells papers at a newspaper stand for $0.40. The papers cost her $0.30, giving her a $0.10 profit on each one she sells. From past experience Barbara knows that: a) 20% of the time she sells 150 papers. b) 20% of the time she sells 200 papers. c) 30% of the time she sells 250 papers. d) 30% of the time she sells 300 papers. Assuming that Barbara believes the cost of a lost sale to be $0.05 and any unsold papers cost her $0.30 and she orders 250 papers. Use the following random numbers: 14, 4, 13, 9, and 25 for simulating Barbara's profit. (Note: Assume the random number interval begins at 01 and ends at 00.) Based on the given probability distribution and the order size, for the given random number Barbara's sales and profit are (enter your responses for sales as integers and round all profit responses to two decimal places): Random Number Sales Profit 14 4 13 9 25
- Kofi Abebrese runs a small industrial company that specialize in the production of high standard windows for housing estates. A worker is paid GHC0.9 per hour and can produce two window with an hour. Each window uses a frame costing GHC1 and incur a variable overheads of GHC0.7. Each window sells for GH¢3. Currently, due to the economic condition, work is rather slack and three employees are occupied in carrying out extensive repairs to Kofi Abebrese's own house. Kofi owns a warehouse next to the factory, which had been used as a factory store, in the past. It is now let out on a renewable annual lease of GHC600. A new building company, Allied Consult, which specializes in the production of prefabricated houses has asked Kofi if he would be interested in accepting a contract for GHC30,000 which will be for a year initially, to produced molded internal building sections. Kofi estimates that, the contract will take 13,200 hours of works, or the work of five men for a year, and that…A company owns a 5-year-old turret lathe that has a book value of $23,000. The present market value for the lathe is $18,000. The expected decline in market value is $1,700/year to a minimum market value of $4,080; maintenance plus operating costs for the lathe equal $4,470/year.A new turret lathe can be purchased for $46,000 and will have an expected life of 8 years. The market value for the turret lathe is expected to equal $46,000(0.70)k at the end of year k. Annual maintenance and operating cost is expected to equal $1,900. Based on a 12% MARR, should the old lathe be replaced now? Use an equivalent uniform annual cost comparison, a planning horizon of 7 years, and the cash flow approach.EUAC for keeping old turret lathe: $EUAC for replacing turret lathe: $In an oil company, its south refinery produces per day 300 barrels of high grade oil, 200 barrels of medium grade oil and 150 barrels of low grade oil. The cost of operation of this refinery amounts to P 600,000 per day. The north refinery of the company produces each day 100 barrels of high grade oil and 100 barrels of medium-grade oil and 150 of low-grade oil. Which has a total of P500,000 operational costs. If the company’s production requirement is at least 900 barrels for high-grade oil, 800 barrels for medium-grade oil, and 750 for low-grade oil, how many days, are required for each refinery to operate to obtain the minimum cost?
- There are two companies manufacturing drones. Company A manufactures mass market drones, while company B manufactures customised drones according to customers’ requirements. In 2020, company A produces 3,200 drones, 3% of which were found to be defective and cannot pass the quality check. Company A employs 5 workers working an average of 8 hours a day in the drone production, and they worked 200 working days in 2020.In contrast, company B produces 900 drones, 10% of which were found to be defective and cannot pass the quality check. Company B employs 3 workers working an average of 6 hours a day in the drone production, and they worked 170 days in 2020. (a) If the drone manufacturing is seen as a process, what is considered as the output of the production processes of companies A and B and why? (b) Measure the single-factor manpower productivity for the two companies. (c) Is it reasonable to compare the manpower productivity of the two companies and reach a conclusion that one company…A farm occupies 200 acres of land and has £10000 available for investment. The family who run the farm can work for a total of 5000 work-hours during the winter and 7000 work-hours for the rest of the year. If any of these work-hours are not needed then the family will use them to help at the local village store, earning a profit of £9 per hour (regardless of the time of year). Past experience shows the family will not have more than 50 spare work-hours to work in the village store during the winter and not more than 80 over the summer. The farm brings in cash for the family from three crops (lettuces, carrots, and swedes) and two types of livestock (dairy cows and hens). The family would like to maximise their cash income. The crops need no investment funds but each cow requires an initial investment of £1000 and each hen £10. Each cow needs 1.5 acres of land and the size of the barn limits the number of cows in the herd to 20. Each cow also require 100 work hours during the winter…During an eight-hour shift, 750 non-defective parts are desired as a result of a manufacturing operation. The default operation time is 15 minutes. As the operators of machine are inexperienced, the actual time they take to perform the operation is 20 minutes, and, on average, a fifth of the parts that start to be manufactured are lost. Assuming that each one of the machines used in this operation will not be available for one hour in each shift, determine the number of machines needed.