A manufacturer produces two sizes of leather handbags. It takes longer to cut and dye the leather for the smaller bag, but it takes more time sewing the larger bag. The production constraints and profit for each type of bag are given in the table.
The machinery limits the number of bags produced to at most
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (4th Edition)
Precalculus
University Calculus: Early Transcendentals (3rd Edition)
- 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_forwardTh 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_forwardJob is on a low cholesterol diet. During lunch at the LST canteen, he always chooses between two meals, Pasta or Tofu. The table below lists the amount of protein, carbohydrates, and vitamins each meal provides along with the amount of cholesterol he is trying to minimize. Job needs at least 180 grams of protein, 930 grams of carbohydrates, and 40 grams of vitamins for lunch each month. Over this time period, how many days should he have the Pasta meal, and how many days the Tofu meal so that he gets the adequate amount of protein, carbohydrates, and vitamins and at the same time minimizes his cholesterol intake? Pasta 89 Tofu 16g 38 g Proteins 55 g Carbohydrates 2g 2g Vitamin C 46 mg 55mg Cholesterol a. Define the variables used and formulate the linear programming model for this problem.arrow_forward
- The amount of nitrogen (in lb/acre), phosphate (in lb/acre), and labor (in hr/acre) needed to grow honeydews, yellow onjons, and lettuce is given by the table to the right. Complete parts a and b. OA. Yes, the farmer should allot B. No, it is not possible to use all resources completely. acres for honeydew, for yellow onions, and acres for lettuce. Honeydews 120 Nitrogen Phosphate 180 Labor 5 a) If the farmer has 230 acres, 30,300 lb of nitrogen, 34,400 lb of phosphate, and 400 hours of labor, is it possible to use all resources completely? If so, how many acres should he allot for each crop? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⒸA. Yes, the farmer should allot acres for honeydew, OB. No, it is not possible to use all resources completely. Yellow onions 150 acres for lettuce. 80 6 Lettuce b) Suppose everything is the same as in part a, except that 1180 hours of labor are available. Is it possible to use all resources…arrow_forwardYour company decides to conduct some production analysis for two of its most popular brands of cups. A carton of Brand X takes 10 hours to produce and 5 hour to package. A carton of Brand Y takes 15 hours to produce and 25 hours to package. If there are exactly 300 hours per month for production and exactly 325 hours per month for packaging, complete the following questions to determine how many cartons of each type of cup will be ready for shipping using all the available time. Create a system of equations for the situation using r for Brand X of cups and y for Brand Y of cups. Equation 1: Equation 2: Graph the system of equations on the grid provided: +30+ 28 26 24 22 20 18 10 14 12 10 2. 4 8 10 12 14 16 18 20 22 24 Clear All Draw:arrow_forwardA diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?arrow_forward
- Flint lab produces 4 high tech product types. Each of the products must be wired, drilled, assembled and checked for quality standard before being delivered to consumers. The time requirement and profit for each product are as follows. Product A: 0.5 hr for wiring, 3 hrs for drilling, 1 hr for assembling, and 0.5 hr for inspection. One product A can be sold for $10 per unit. Product B: 1.5 hr for wiring, 1 hrs for drilling, 3 hrs for assembling, and 1 hr for inspection. One product B can be sold for $13 per unit. Product C: 1.5 hr for wiring, 2 hrs for drilling, 3 hrs for assembling, and 0.5 hr for inspection. One product C can be sold for $16 per unit. Product D: 1 hr for wiring, 3 hrs for drilling, 2 hrs for assembling, and 0.5 hr for inspection. One product D can be sold for $12 per unit. The maximum capacity for wiring, drilling, assembly, and inspection are 1500 hrs; 2350 hrs; 2600 hrs; and 1200 hrs respectively. Flint lab requires that there will be at least 150 units of A, 100…arrow_forwardA contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Hauling Cost per Ton at Site Pit 1 3 Price per Ton North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site. a. Formulate this problem as an assignment problem by constructing the appropriate cost table,…arrow_forwardA company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…arrow_forward
- The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost? Type A Type B Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5arrow_forwardA toy factory creates miniature steel train engines and box cars. The fabrication department has 5,279 minutes available per week and the assembly and finishing department has 5,999 minutes available per week. Manufacturing one miniature steel train engine requires 12 minutes of fabrication and 10 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 6 minutes of fabrication and 10 minutes of assembling and finishing. The profit on each miniature steel train engine is $9.50 and the profit on each miniature steel box car is $8.25. How many steel train engines and steel box cars should be produced each week to obtain the maximum profit? Find the maximum weekly profit. (Use x for box car and y for train engine.) Maximize P = ≤5, 279 5,999 subject to Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round toys to…arrow_forwardA.Quinn:15 hours Jack:3.75 hours B.Quinn:3hours Jack:12 hours C.Quinn:3.75 hours Jack:15 hours D.Quinn:1.5 hours Jack:1.5 hoursarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell