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- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.What is the total effect on the economy of a government tax rebate of $500 to each household in order to stimulate the economy if each household will spend of the rebate in goods and services?The Newcoat Painting Company has for some time been experiencing high demand for its automobile repainting service. Because it has had to turn away business, management is concerned that the limited space available to store cars awaiting painting has cost them in lost revenue. A small vacant lot next to the painting facility has recently been made available for rental on a long-term basis at a cost of $10 per day. Management believes that each lost customer costs $20 in profit. Current demand is estimated to be 21 cars per day with exponential interarrival times (including those turned away), and the facility can service at an exponential rate of 24 cars per day. Cars are processed on a FCFS basis. Waiting space is now limited to 9 cars but can be increased to 20 cars with the lease of the vacant lot. Newcoat wants to determine whether the vacant lot should be leased. Management also wants to know the expected daily lost profit due to turning away customers if the lot is leased. Only…
- A multimedia company anticipates that there will be a demand for 20,000 copiesof a certain DVD during the next year. It costs the company $0.40 to store a DVD for one year. Each time it must make additional DVDs, it costs $250 to set up the equipment. How many DVDs should the company make during each production run to minimize its total storage and setup costs?Ocean water contains 0.9 ounces of gold per ton. Method A costs $550 per ton of waterprocessed and will recover 90% of the metal. Method B costs $400 per ton of waterprocessed and will recover 60% of the metal. The two methods require the same capitalinvestment and are capable of producing the same amount of gold each day. If the extractedgold can be sold for $1,750 per ounce, which method should be recommended? The supplyof ocean water is essentially unlimited.Sleep-EZ Manufacturing Company produces high end home furniture. Sleep-EZ must determine how many units of its Recline-O-Matic chairs to produce each month for the next 3 months. The beginning inventory of finished chairs on August 1 is 100 units. Demand for the chairs is expected to be 1,500 units in August, 2,400 units in September, and 1,800 units in October. Sleep-EZ wants to have 275 completed chairs on hand at the end of October. Production cost is $1,000 per chair in August and is expected to increase by 10% each month. In addition, storage cost from one month to the next is $80 per chair. Due to raw material and labor constraints, the maximum number of chairs Sleep-EZ can produce each month is 2,400, 1,600, and 2,200, respectively. Prepare and solve a linear programming model to determine the production schedule for August, September, and October that will minimize total cost while meeting demand in each month. (Hint: Remember Beg Inv + Prod - Sales = End Inv. You can create…
- A company in Hungary manufactures and sell the product "Mini Bike". The company operates at maximum capacity, producing seven days a week, which makes 50 000 units per year. (To make it simple, we assume that a year has 50 weeks.) The value of a Mini Bike unit leaving production is €100. The cost of capital is estimated to 20%. The cost for holding inventory is 15%, which gives a total inventory carrying cost percentage of 35%. No safety stock is kept in Hungary. Mini Bike is distributed to a wholesaler in the UK, where it's sold to the end customers. There are two transportation alternatives - by rail or by truck: . By rail means a dispatch every 14 days. The transportation time is one week. The cost is €4/unit. . By truck means a dispatch every week. The transportation time is two days. The cost is €6/unit In the UK, the wholesaler has a safety stock corresponding to half a week of sales. Which distribution alternative gives the lowest total cost when considering the transportation…ABC Company is considering constructing a plant to manufacture a proposed new product. The land costs P15,000,000, the building costs P30,000,000, the equipment costsP12,500,000, and P5,000,000 capital is required. At the end of 12 years, the land can be sold for P25,000,000, the building for P12,000,000, the equipment for P250,000, and all of the working capital recovered. The annual disbursements for labor, materials, and all other expenses are estimated to cost P23,750,000. If the company requires a minimum return of 25%, what should be the minimum annual sales for 12 years to justify the investment?A retired couple wishes to invest $750,000, diversifying the investment in three areas: a high-risk stock that has an expected annual rate of return (or interest) of 12%, a low-risk stock that has an expected annual return of 8%, and government-issued bonds that pay annual interest of 4% and involve no risk. To protect the value of the investment, the couple wishes to place at least twice as much in the low-risk stock as in the high-risk stock and use the remainder to buy bonds. How should the money be invested to maximize the expected annual return?