1. Sporting Goods Product Mix. Kelson Sporting Equipment, Inc. makes two types of baseball gloves: a regular model and a catcher's model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Cutting Packaging Model and Finishing and Profit/Glove Sewing Shipping Regular 1/2 1/8 $5 1 model Catcher's 3/2 1/3 /4 $8 model
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Assume the availability in the finishing and packaging departments are 350 and 125 hours respectively.
What is the optimal maximum profit?
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- #1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…Amy Zeng, owner ofZeng's Restaurant Distributions,supplies nonperishable goods to restaurants around the metroarea. She stores all the goods in a storage area with a single dockand one aisle. The goods are divided into five categories accordingto the following table. The table indicates the number of tripsper month to store or retrieve items in each category, as well asthe number of storage blocks taken up by each. The following picture of the storage area provides an identificationnumber for each of the 16 storage blocks. For each item category,indicate into which blocks it should be stored.
- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.Fliptop Model Tiptop Model AvailablePlastic 3 4 36Ink Assembly 5 4 40Molding Time 5 2 30The profit for either model is $1000 per lot.What is the linear programming model for this problem?What are the boundary points of the feasible region?What is the profitability at each boundary point of the feasible region?Find the optimal solution.ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.Accompany makes two products (1&2) each product requires time on two machines (A&B). specification for each product is as follows. Product1 product2 Processing time on Machine A (hrs/unit) 2 2 Processing time on Machine B (hrs/unit) 1 2 Material and labour cost ( ksh/unit) 14 15 Selling price (ksh/unit) 16 18 Maximum possible sale (units) 130 150 The amount of time available on machine A is 360 hours and on machine B is 260 hours. Formulate the linear programme which, when…
- Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 4 4 5 4 5 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) The minimum number of workers is 7 workers. (Enter your response as a whole number.) Specify the workforce schedule for each employee by indicating the day offs (other days are considered to be…Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 5 5 6 2 2 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) Part 2 The minimum number of workers is _________workers. (Enter your response as a…
- Polly Astaire makes fine clothing for big and tall men. A fewyears ago Astaire entered the sportswear market with theSunset line of shorts, pants, and shirts. Management wants tomake the amount of each product that will maximize profits.Each type of clothing is routed through two departments, Aand B. The relevant data for each product are as follows: Department A has 120 hours of capacity, department B has160 hours of capacity, and 90 yards of material are available.Each shirt contributes $10 to profits and overhead; each pairof shorts, $10; and each pair of pants, $23.a. Specify the objective function and constraints for thisproblem.b. Use a computer package such as POM for Windows tosolve the problem.c. How much should Astaire be willing to pay for an extrahour of department A capacity? How much for an extrahour of department B capacity? For what range of right-hand values are these shadow prices valid?A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?b. What is the maximum price the store would be justified in paying for additional pine bark?c. What is the marginal value of labor? Over what range is this value in effect?d. The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?e. If the manager can obtain either additional pine bark or additional storage space, which oneshould she choose and how much (assuming…A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?