How many machines of each class must the company purchase to reach its target
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TOPIC: LINEAR PROGRAMMING (CASE WITH MORE THAN TWO VARIABLES FOR SIMPLEX METHOD)
A company is considering the acquisition of additional machinery as part of a capital expansion program.
expansion program. Four types of machines are being considered. The following table specifies the attributes pertinent
to each of them:
[Table]
The total budget for the program is $6,000,000.00 and the maximum space available is 290 square meters.
square meters. The company wants to maximize the production that will be achieved in the purchase of the new machines.
A) How many machines of each class must the company purchase to reach its target?
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- 4. A publisher prints copies of a popular weekly tabloid for distribution and sale. The fixed costs are $500 per print run, with each copy printed costing an additional $0.40. If C(q) is the cost function (in $) of the price of the print run as a function of copies printed, what is the formula for C(q)? Select one: a. C(q) = 500 + 0.4q b. C(q) = 500q + 0.4 c. C(q) = (500 + 0.4)q d. C(q) = 500 - 0.4q e. C(q) = 500q - 0.4 5. A hot dog vendor sells an average of 50 hot dogs during a Little League baseball game. If the sales are Normally distributed with a standard deviation of 7 hot dogs, what is the probability the vendor will sell between 45 and 65 hot dogs? Select one: a. 74.50% b. 92.36% c. 99.78% d. 174.50% e. 2.14 f. -0.71 g. 0.71We all hate to bring small change to the store. Usingrandom numbers, we can eliminate the need for change andgive the store and the customer a fair shake.a Suppose you buy something that costs $.20. How could you use random numbers (built into the cash reg-ister system) to decide whether you should pay $1.00 or nothing? This eliminates the need for change!b If you bought something for $9.60, how would youuse random numbers to eliminate the need for change?c In the long run, why is this method fair to both thestore and the customer?3-4) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E + 30 3-5) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00 D) $158.18
- Assume the demand for a company’s 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 soldfor $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.Company X produces a product, GlueX3, that Company X sales for $5. An opportunity presents itself to reallocate its manufacturing facility and related resources to produce Epoxy10. It believes it can sell Epoxy10 for $8. Explain how this switch creates “value”. Be sure to include for whom.Joe is selling Christmas trees to pay his college tuition.He purchases trees for $10 each and sells them for $25each. The number of trees he can sell is normally distributedwith a mean of 100 and standard deviation of 30. How manytrees should Joe purchase?
- An optometrist orders eyeglass frames at a cost of $40per frame and sells each frame for $70. Annual holding costis 20% of the optometrist’s cost of purchasing a frame. Eachtime frames are ordered, a cost of $200 is incurred. Becauseof lost goodwill, a cost of $50 is incurred each time acustomer wants a frame that is not in stock. Frames aredelivered one week after an order is placed. Annual demandfor frames is N(1,040, 15.73).a Assuming all shortages are backlogged, determinethe order quantity and reorder point. b Assuming all shortages result in lost sales, deter-mine the order quantity and reorder point. c To meet 95% of all orders from stock, what shouldbe the reorder point?d To have shortages occur during an average of twolead times per year, what should be the reorder point?If a company employs n salespersons, its gross sales in thousands of dollars may be regarded as a random vari-able having a gamma distribution with α = 80√n and β = 2. If the sales cost is $8,000 per salesperson, how many salespersons should the company employ to maxi-mize the expected profit?you are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it cost $0.03 per copy to operate the copier. Other fixed costs of running the store withh amount to $400 per month. You plan to charge $0.10 per copy, and the store will be open 365 days per year. Each copier can make up to 100,000 copies per year. a. for one to five copiers rented and daily demands of 500, 1000, 1500, 2000 copies perday, find annual profit. That is, find annual profit for each of these combinations of copiers rented and daily demand. b. if you rent three copies, what daily demand for copies will allow you to break even? c. Graph profit as a function of the number of copiers for a daily demand of 500 copiers; for a daily demand of 2000 copies. Interpret your graph
- write a linear program that will maximize profits. You don’t need to solve it. Hint: Define your variables as: Xij = tons of commodity i loaded into cargo hold jYour company makes hand sanitizer in two lines: Moisturizing+, and StandardSoap. On the market, Moisturizing+ retails for $175/L and StandardSoap retails for $95/L. You make the hand sanitizer by combining lotion, soap, and secret ingredient SpecialX. These ingredients are purchased from a mysterious supplier, and you can purchase at most 4000L of lotion, 5000L of soap, and 750L of SpecialX in a month. Lotion costs $25/L, soap costs $10/L, and SpecialX costs $35/L. To make 1L of Moisturizing+, you need to combine 0.5L of lotion, 0.3L of soap, and 0.2L of SpecialX. To make 1L of StandardSoap, you need to combine 0.4L of lotion, 0.55L of soap, and 0.05L of SpecialX. Your company has committed to donating 500L of StandardSoap to a local charity. Since this is a donation, you will not receive any revenue. However, the costs and purchasing limits apply to both the hand sanitizer that is sold on the market and donated to charity. You want to maximize your monthly profit. Assume that…Month Sales January 250 February 350 March 240 April 260 May 280 June 330 July 220 August 310 September 235 October 300 November 240 December 230 A.What is the value of MSE (mean squared error)? The answer is . (Make sure no decimal place and no comma. EX: 1234) B.What is the optimal alpha value to minimize inaccuracy? The answer is . (Make sure two decimal places.)