Field, Bell and Weiss, a consulting firm, has been engaged by the Fizzle Beverage Company to determine possible methods for expanding their warehouse facilities. The current warehouse has 16' ceilings with a possible 10' clear stacking height. At the 10' level the obstructions are steam pipes, lighting fixtures and air ducts. Fizzle Beverage currently receives all pallets by truck. Each pallet load is 6' high (including the pallet). To take full advantage of all available height the second level pallet in each stack must be broken down. Question: How could Fizzle increase storage capacity?
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- The manager of the deli section of a grocery superstore has just learned that the department has112 pounds of mayonnaise, of which 70 pounds is approaching its expiration date and must beused. To use up the mayonnaise, the manager has decided to prepare two items: a ham spread anda deli spread. Each pan of the ham spread will require 1.4 pounds of mayonnaise, and each panof the deli spread will require 1.0 pound. The manager has received an order for 10 pans of hamspread and 8 pans of the deli spread. In addition, the manager has decided to have at least 10 pansof each spread available for sale. Both spreads will cost $3 per pan to make, but ham spread sellsfor $5 per pan and deli spread sells for $7 per pan.a. Determine the solution that will minimize cost.b. Determine the solution that will maximize profit.A manufacturing fi rm has discontinued production of a certain unprofi table product line.Considerable excess production capacity was created as a result. Management is consideringdevoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit areProductMachine Type X1 X2 X3Milling machine 8 2 3Lathe 4 3 0Grinder 2 0 1The available time in machine hours per week isMachine Hours per WeekMilling machines 800Lathes 480Grinders 320The salespeople estimate they can sell all the units of X1 and X2 that can be made. Butthe sales potential of X3 is 80 units per week maximum.Unit profi ts for the three products areUnit ProfitsX1 $20X2 6X3 8a. Set up the equations that can be solved to maximize the profi t per week.b. Solve these equations using the Excel Solver.c. What is the optimal solution? How many of each product should be made, and whatshould the resultant profi t be?d. What is this situation with respect to the machine groups? Would they…19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5
- ABC Cabinets received a contract to produce bookshelf speakers (BS) and floor speakers (FS) over the next 2months. The contract says ABC must deliver 2100 BS and 1500 FS at the end of month 1 and deliver 1200 BS and2600 FS at end of month 2. The time to make a BS is 0.7hr and a FS is 1hr. Raw material costs $10 for each BSand $12 for each FS and there is an unlimited amount available. Labor costs are $22/hr using regular productiontime and $33/hr using overtime. ABS has up to 2400hrs of regular production time each month and up to 1000additional hours of overtime each month. Any cabinets left at the end of month 1 can be stored for $5/cabinet.(a) Formulate an LP to determine the number of units that should be manufactured each month on regular andovertime to minimize total production and storage costsJenny Company produces two types of pants: long pants and short pants. The cost of making apair of short pants and a pair of long pants are RM 75 and RM 95 respectively. In one week, thecompany must produce at least 150 pants of each type. The minimum weekly production is 500pants. The short pants are sold for RM 120 each and the long pants for RM 150 each. Using thegraphical method, find:a. The number of short pants and long pants to be made in a week in order to minimise thetotal production cost.b. The profit made at the minimum weekly production cost.Production and Materials Purchases Budgets White Corporation’s budget calls for the following sales for next year:Quarter 1 90,000 units Quarter 3 68,000 unitsQuarter 2 76,000 units Quarter 4 96,000 unitsEach unit of the product requires 3 pounds of direct materials. The company’s policy is to begineach quarter with an inventory of product equal to 5% of that quarter’s estimated sales requirementsand an inventory of direct materials equal to 20% of that quarter’s estimated direct materials requirements for production.Required Determine the production and materials purchases budgets for the second quarter.
- The Johnny Ho Manufacturing Company inColumbus, Ohio, is putting out four new electronic components. Each of Ho’s four plants has the capacity to add one more prod-uct to its current line of electronic parts. The unit-manufacturing costs for producing the different parts at the four plants areshown in the accompanying table. How should Ho assign the newproducts to the plants to minimize manufacturing costs?ELECTRONICCOMPONENT PLANT123 4C53 $0.10 $0.12 $0.13 $0.11C81 0.05 0.06 0.04 0.08D5 0.32 0.40 0.31 0.30D44 0.17 0.14 0.19 0.15Ronald and Son, P.A., is an auditing firm that conducts both financial and operational audits. Ronald can conduct 90 financial audits (FAs) per year if he spends full time on just FAs, or 180 operational audits (OAs) per year full time, or any linear combination of both. (Note: A linear combination means that because the capacity required for 1 FA is the same as that for 2 OAs (90 to 180 ratio), Ronald can conduct such combinations as 89 FAs plus 2 OAs, or 88 FAs plus 4 OAs, and so on.) Son processes the reports made by Ronald. Son can prepare 180 financial audit reports or 150 operational audit reports per year, or any linear combination thereof. The office staff finalizes the reports submitted by Son. They can handle no more than 160 reports of any kind, per year. Ronald and Son have calculated that to keep their association solvent, they must produce at least 30 FAs and 50 OAs each year. The profit from each FA has averaged $720 in the past and for each OA has been about $650. How…A chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, andchocolates.A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a…
- 46. Ford is going to produce a new vehicle, the Pioneer,and wants to determine the amount of annual capacityit should build. Ford’s goal is to maximize the profitfrom this vehicle over the next five years. Each vehicle will sell for $19,000 and incur a variable production cost of $16,000. Building one unit of annual capacity will cost $2000. Each unit of capacity will alsocost $1000 per year to maintain, even if the capacityis unused. Demand for the Pioneer is unknown butmarketing estimates the distribution of annual demandto be as shown in the file P09_46.xlsx. Assume thatthe number of units sold during a year is the minimumof capacity and annual demand. Which capacity levelshould Ford choose? Do you think EMV is the appropriate criterion?Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?A wood products firm uses available time at the end of each week to make goods for stock.Currently, two products on the list of items are produced for stock: a chopping board and a knifeholder. Both items require three operations: cutting, gluing, and finishing. The manager of thefirm has collected the following data on these products.TIME PER UNIT (MINUTES)Item Profit/Unit Cutting Gluing FinishingChopping board $2 1.4 5 12Knife holder $6 0.8 13 3The manager has also determined that, during each week, 56 minutes are available for cutting, 650minutes are available for gluing, and 360 minutes are available for finishing.a. Determine the optimal quantities of the decision variables if the goal is to maximize profit.b. Which resources are not completely used by your solution? How much of each resource isunused?