Inventory Costs A warehouse operator has 24,000 square feet of floor space in which to store two products. Each unit of product I requires 20 square feet of floor space and costs
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- Shipping A warehouse supervisor has instructions to ship at least 50 bags of gravel that weigh 55 pounds each and at least 40 bags of stone that weigh 70 pounds each. The maximum weight capacity of the truck being used is 7500 pounds. (a) Write and graph a system that describes the numbers of bags of stone and gravel that can be shipped. (b) Find two solutions of the system and interpret their meanings in the context of the problem.arrow_forwardPlease TYPE YOUR WORKarrow_forwardBibbins Manufacturing produces softball and baseballs for youth recreation leagues. Each softball costs $11 to produce and sells for $17 while each baseball costs $10.50 and sells for $15. The material and labor required to produce each item is listed here along with the availability of each resource. Amount Required Per Amount Resource Softball Baseball Available Leather 5 oz 4 oz 6,000 oz Nylon 6 yds 3 yds 5,400 yds Core 4 oz 2 oz 4,000 oz Labor 2.5 min 2 min 3,500 min Stitching 1 min 1 min 1,500 min If X, = number of softballs to produce, X, = number of baseballs to produce, what is the objective function? МАХ 6 X, +4.5 X2 MIN 6X, + 4 X2 МАX 11 X, + 17 X2 МAX 2.5 X, + 6 X2arrow_forward
- ANSWER THE FOLLOWING A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000 hours are available for producing the parts, 4000 hours for assembling the parts and 5500 hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110. Set T1 = X1 ; T2 =X2 ; Z=Profit Profit Equation would be: a. Z= 90 x1 + 110 x2 b. Z= 1.5 x1 + 2.5 x2 c. Z= 2 x1 + 3 x2 d. Z= 110 x1 + 90 x2 (2) The solution set of the system of inequalities are the following, except? a. x1+2.5x2≥4000 b. 2x1+1.5x2≤5500 c. x1≥0 d. 2x1+4x2≤7000 (3) How many of type A of tables should be produced in order to maximize the total monthly profit? a. 2,300 b. 2,750 c. 1,750 d. 1,500 (4) How many of type B of tables should be produced in order to maximize the total…arrow_forwardAssistance please with the following: showing all working.arrow_forwardOperations Research 1Do as Indicatedarrow_forward
- Th have $150,000 available to purchase additional equipment and 250 square feet of floor space to install the new equipment. They can purchase a lathe, a press, a grinder, a metal bender, a shearing table, or some combination of the above. The company can only purchase one of each item, but they Manufacturing Company is looking to expand their production capabilities. They may purchase as many of items as they can afford. The cost and square footage for each machine is detailed in the table below. Name Cost Square Footage Lathe (x1) $45,000 50 sq ft Press (x2) $65,000 80 sq ft Grinder (x3) $30,000 120 sq ft Metal Bender (x4) $75,000 70 sq ft Shearing Table (x5) $15,000 80 sq ft The company estimates they can generate a profit each day from each piece of equipment of $800 from the lathe, $600 from the press, $1,400 from the grinder, $1.200 from the metal bender, and $400 from the shearing table. Unfortunately, the manufacturing company only has the safety permit to install the lathe or…arrow_forwardIt takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements. The meat contains 2 units of carbohydrates and 2 units of protein per pound. The cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.40 per pound and the cheese costs $4.50 per pound. How many pounds of each are needed to fulfill the minimum requirements at minimum cost? What is Jacob's minimum cost? He should buy pound(s) of meat and pound(s) of cheese. (Round your answer to the nearest tenth.) The minimum cost is $. (Round to the nearest cent as needed.) ...arrow_forwardExplain Linear Systems?arrow_forward
- Customers arrive at the ticket counter of a local movie theater at a rate of 240 persons per hour, at 5.30 PM. After 10 minutes, the arrival rate declines to 60 persons per hour and continues at that level for 20 minutes. If the service rate is 2.5 persons/minute. (3)a.Describe the performance of the system, assuming that all the factors remain the same. (Longest queue, longest delay, total delay, average delay/person, etc.)b.Draw a neat sketch of the system. (Apply the D/D/1 model)arrow_forwardA large department store needs at least 3600 labor hours covered per week. It employs full-time staff 40 hr/wk and part- time staff 25 hr/wk. The cost to employ a full-time staff member is more because the company pays benefits such as health care and life insurance. Hours per Week Cost per Hour Full time 40 hr $25 Part time 25 hr $18 The store manager also knows that to make the store run efficiently, the number of full-time employees must be at least 1.25 times the number of part-time employees. a. Determine the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost. b. What is the minimum weekly cost to staff the store under these constraints?arrow_forwardNutrition Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 248 grams of protein and at least 168 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.) grain oz chicken oz Need Help? Watch It Read Itarrow_forward
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