A bicycle manufacturer makes mountain bikes and road bikes. Each mountain bike requires 2 units of steel and 6 units of aluminum in its frame and 12 special components for the hub, sprocket, and gear assembly. Each road bike requires 5 units each of steel and aluminum for its frame and 5 of the special components. Shipments are such that steel is limited to 114 units per day, aluminum is limited to 142 units per day, and the special components are limited to 214 units per day. If the profits are $500 on each mountain bike and $400 on each road bike, how many of each should be produced to yield the maximum profit?

A company produces three types of bookcases: Standard, Deluxe, and Premium. Each bookcase must be sanded, assembled and painted. The Standard model requires 1 hour to sand, 2 hours to assemble, and 1 hour to paint. The Deluxe model requires 2 hours to sand, 3 hours to assemble and 1 hour to paint. The Premium model requires 1 hour to sand, 4 hours to assemble and 2 hours to paint. There are 170 hours available for sanding, 320 hours for assembling and 130 hours for painting. How many of each product can be made? Solve using cramers rule. a. wriite the system of equations for this information. identify variables  b. write and label each of the four determinants, do not evaluate. c. solve for only the first variable in the system. use co-factors and minors to solve the d determinant. label the answer

The 1-Dream company makes two different BLU-ray players, which are assembled on two different assembly lines. Line 1 can assemble 40 units of the BLU-Ray player and 55 units of the BLU-Ray player with DVR per hour, and line 2 can assemble 110 units of the BLU-Ray player and 195 units of the BLU-Ray player with DVR per hour. The company needs to produce at least 3,989 BLU-Ray players and 6,755 BLU-Ray player with DVR to fill an existing order. It cost $100 per hour to run line 1 and $310 per hour to run line 2, how many hours should each line run to fill the order at minimum cost? (Use x for line 1 hours and y for line 2 hours.) Minimize C= ≥ 3,989 6, 755 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 hours to 1 decimal place and cost to 2 decimal places. Number of hours to run line 1 is Minimum cost is $ Number of hours to run line 2…

38) SET UP ONLY: A business has 3 machines that manufacture containers. Together they can make 100 containers per day, whereas the two fastest machines can make 80 containers per day. The fastest machine makes 34 more containers per day than the slowest machine. How many containers can each machine make per day?

Hello Dolly, Inc. crafts three styles of dolls: Lexi, Maysy, and Dizzy. Each doll requires sewing time, painting time, and supplies. Sewing machines are available for only 118 hours, only 2805 hours are available for painting, and 390.5 lbs. of supplies are available. Each Lexi doll requires 0.2 hours of sewing, 9 hours of painting, and 0.7 lbs. of supplies. Each Maysy doll requires 0.4 hours of sewing, 10 hours of painting, and uses 0.9 pounds of supplies. Each Dizzy doll requires 0.5 hours of sewing, 7 hours of painting, and 2 pounds of supplies. If the company earns a profit of $145 per Lexi doll, $155 per Maysy doll, and $150 per Dizzy doll, how many of each doll should the company produce to maximize profit? How much profit will result? (Use for the number of Lexi dolls, y for the number of Maysy dolls, and z for the number of Dizzy dolls.) Maximize P = subject to ≤118 ≤2805 <390.5 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes…

A manufacturer of table saws has three models-Deluxe, Premium, and Ultimate-that must be painted, assembled, and packaged for shipping. The table gives the number of hours required for each of these operations for each type of table saw. If the manufacturer has 104.1 hours available for painting, 360 hours for assembling, and 123.2 hours for packaging, how many of each type of saw can be produced each day? Deluxe 1.2 Painting Assembling 3 Packaging 0.4 Premium Ultimate 2 2.3 7 8 0.9 3 The manufacturer can produce deluxe saws, premium saws, and ultimate saws.

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?

Each week at a furniture factory, 2000 work hours are available in the construction department, 1400 workhours in the painting department, and 1300 work hours in the packing department. Producing a chairrequires 2 hours of construction, 1 hour of painting, and 2 hours for packing. Producing a table requires 4hours of construction, 3 hours of painting, and 3 hours for packing. Producing a chest requires 8 hours ofconstruction, 6 hours of painting, and 4 hours for packing. If all available time is used in every department,how many of each item is produced each week? Do not solve this problem, just write the augmentedmatrix associated with this problem. Specify each variable used in the equation.