Sophie G. Inc. makes three types of bicycle frames: cruiser, road, and mountain bike. Each framerequires units of aluminum tubing and units of steel tubing as shown in the table below.CruiserMountainAluminumSteel517Road1210430The company has available 2000 units of aluminum tubing per week and 9000 units of steeltubing per week. The company makes $40 profit on each cruiser frame, $60 profit on each roadframe and $40 profit on each mountain bike frame. How many of each type should the companymake in order to maximize weekly profits? (round your answers to the nearest whole frame).

Answered: Image /qna-images/answer/1d17b451-87c0-404a-9595-d54186731762.jpg

Answered: Sophie G. Inc. makes three types of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Laura is planning to buy three 5-lb bags of sugar, six 5-lb bags of flour, three 1-gal cartons of milk, and six 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows. A = Sugar (5-lb bag) $3.15 $2.99 $3.74 B = Flour (5-lb bag) $3.79 $2.89 $2.98 Supermarket I Supermarket II Supermarket III (a) Write a 3 x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets. Milk (1-gal carton) $2.99 $2.79 $2.89 C = Eggs (1-dozen carton) $3.49 $3.29 $2.99 (b) Write a 4 x 1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarkets. (c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket.
A forest consists of two types of trees; young (between 0 and 3 m tall) and adults (more than 3 m). Each year, 20% of young trees die, 10% sell for $20 each, 30% remain between 0 and 3 m, and 40% grow taller than 3 m. Each year, 40% of adult trees sell for $50, 20% sell for $20, 30% remain in the forest, and 10% die. What percentage of the trees planted sell for $50?
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.
A 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…
A researcher believed that the number of rental cars in service by a car rental company would have an impact on the total annual revenue for that car rental company. Five small car rental companies were surveyed, with the number of Cars in service recorded in units of 1000 (so if a car rental company had 54000 cars in service, a 54 would be recorded) and Annual Revenue measured in millions of dollars (so an Annual Revenue of $10,000,000 would be recorded as 10). The data follows: Cars (1,000s) Annual Revenue ($ millions)11.5 118 10.0 135 9.0 100 5.5 37 3.3 32 Part of the Excel-generated Simple Linear Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 7891.863897 7891.863897 22.91180151 0.017339231 Residual 3 1033.336103 344.4453677 Total 4 8925.2 Coefficients Standard Error t Stat P-value Intercept -19.12490108 23.1658578…
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 2000 units of product A, up to 3000 units of product B, and up to 5000 units of prod-uct C. Each unit of product C uses two units of A and three units of B and incurs $7 in processing costs. Prod-ucts A and B are produced from either raw material 1 or raw material 2. It costs $9 to purchase and process one unit of raw material 1. Each processed unit of raw mate-rial 1 yields two units of A and four units of B. It costs $5 to purchase and process a unit of raw material 2.Each processed unit of raw material 2 yields one unit ofA and three units of B. The unit prices for the products are: A, $10; B, $9; and C, $32. The quality levels ofeach product are: A, 7; B, 9; and C, 6. The average quality level of the units sold must be at least 8. Deter-mine how to maximize Bexter’s profit.
In a factory, machines R, S and T are all producing metal rods of the same length. Machine R produces 35% of the rods, machine S produces 40% and the rest are produced by machine T. Of their production of rods, machines R, S and T produce 4%, 5% and 3% defective rods respectively.
A supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three Day
A computer manufacturer buys 30% of its chips from supplier A and the rest from supplier B. Two percent of the chips from supplier A are defective, as are 4% of the chips from supplier B. Approximately what percentage of the defective chips are from supplier B?
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.

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