A manufacturing plant makes two types of inflatable boats––a two-person boat and a four-person boat. Each two-person boat requires
(A) Identify the decision variables.
(B) Summarize the relevant material in a table similar to Table 1 in Example 1.
(C) Write the objective function
(D) Write the problem constraints and nonnegative constraints.
(E) Graph the feasible region. Include graphs of the objective function for
(F) From the graph and constant-profit lines, determine how many boats should be manufactured each month to maximize the profit. What is the maximum profit?
Trending nowThis is a popular solution!
Chapter 5 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Additional Math Textbook Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Mathematical Ideas (13th Edition) - Standalone book
Thinking Mathematically (6th Edition)
Mathematics All Around (6th Edition)
Finite Mathematics & Its Applications (12th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
- A car wash offers the following optional services to the basic wash: clear coat wax, triple foam polish, undercarriage wash, rust inhibitor, wheel brightener, air freshener, and interior shampoo. How many washes are possible if any number of options can be added to the basic wash?arrow_forwardIf a man has 4 sweaters and 5 pairs of slacks, how many different outfit can he wear?arrow_forwardA commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The commuter likes to vary the trip as much as posible, so she alwaysleaves and returns by different roads. In how many different ways can she make the round-trip?arrow_forward
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardA high school dietician is planning menus for the upcoming month. Anew item will be spaghetti with sauce. The dietician wants each serving tocontain at least 10 grams of protein and at least 40 grams of carbohydrates.Spaghetti contains 5 grams of protein and 32 grams of carbohydrates per cup,and the sauce contains 4 grams of protein and 5 grams of carbohydrates percup. For aesthetic reasons, the dietician wants a ratio of spaghetti to sauce to be4:1.Spaghetti costs $0.30 per cup to buy and prepare, and the sauce $0.40 per cupto buy and prepare. The dietician wants to minimize the cost per serving andkeep the calories per serving 330 or less. The sauce contains 100 calories percup, and spaghetti contains 160 calories per cup.Formulate a linear programming model for this problem.arrow_forwardThe Donaldson Furniture Company produces three types of rocking chairs: the children's model, the standard model, and the executive model. Each chair is made in three stages: cutting, construction, and finishing. Stage Cutting Construction Finishing Children's Standard Executive 7 hr 5 hr 4 hr 3 hr 2 hr 5 hr 2 hr 2 hr 4 hr The time needed for each stage of each chair is given in the chart. During a specific week the company has available a maximum of 166 hours for cutting, 106 hours for construction, and 84 hours for finishing. Determine how many of each type of chair the company should make to be operating at full capacity. The number of executive chairs the company should make isarrow_forward
- The Cheery Cherry Chair Company makes three types of chairs, the Montegue, the Capulet, and the Verona. Each chair requires assembly, finishing, and a certain amount of wood to make. The assembly area can be used for at most 10 hours per day. To keep him busy, the finishing person needs to work at least 6 hours per day. Producing a Montegue requires 1 hour of assembly, 2 hour of finishing, and 9 board feet of wood. Producing a Capulet requires 1 hour of assembly, 1 hour of finishing, and 9 board feet of wood. Finally, producing a Verona requires 2 hour of assembly, 1 hour of finishing, and 3 board feet of wood. If the company wants to minimize the amount of cherry wood used, how many should they make of each model? (It is possible to complete a fractional part a chair in a given day; in the long run you end up with completed chairs.) Number of Montegues = Number of Capulets = Number of Veronas = How many board feet of cherry wood would be used each day?arrow_forwardA furniture manufacturer, makes chairs coffee tables and dining room tables. Each chair requires 10 minutes of sanding, 6 minutes of staining, and 12 minutes of varnishing.Each coffee requires 12 minutes of sanding, 8 minutes of staining, and 12 minutes of varnishing.Each dining-room table requires 15 minutes of sanding, 12 minutes of staining, and 18 minutes of varnishing. The sanding bench is available 16 hours per week, the staining bench 11 hours per week, and the varnishing bench is 18 hours per week. How many of each type of furniture should be made per week so that the benches are fully utilized? (Use Gaussian Reduction Method)arrow_forwardA manufacturer of lightweight mountain tents makes a standard model and an expeditionmodel for national distribution. Each standard tent requires 1 labour hour from the cuttingdepartment and 3 labour hours from the assembly department. Each expedition tent requires 2labour hours from the cutting department and 4 labour hours from the assembly department.The maximum labour hours available per day in the cutting department and the assemblydepartment are 32 and 84 respectively. If the company makes a profit of E50 on each standardtent and E80 on each expedition tent, use the graphical method to determine how many tentsof each type should be manufactured each day to maximize the total daily profit?arrow_forward
- A furniture store expects to sell 120 coffee tables during the next year. It costs $1.50 to store one coffee table for one year. To reorder, there is a fixed cost of $10, plus $2.80 for each coffee table ordered. In what lot size and how many times per year should an order be placed to minimize inventory costs? coffee tables per order orders per yeararrow_forwardFlint 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 manufacturing firm has received a contract to assemble 1000 units of test equipment in the next year. The firm must decide how to organize its assembly operation. Skilled workers, at $33 per hour each, can individually assemble the test equipment in 2.6 hours per unit. Alternatively, teams of four less skilled workers (at $19 per hour per worker) can assemble a unit in one hour. Which approach is more economical?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning