i. formulate the LP Model;ii. identify the decision variables used in the model; andiii. determine the optimal solution using graphical method.A businessman is considering opening a small specialized trucking firm. To make the firmprofitable, it must have a daily trucking capacity of at least 84,000 cubic feet. Two types of trucksare appropriate for the specialized operation. Their characteristics and costs are summarized inthe table below. Note that truck two requires three drivers for long haul trips. There are 41potential drivers available, and there are facilities for at most 40 trucks. The businessman'sobjective is to minimize the total cost outlay for trucks.СарacityDriversTruckCost(cu. ft.)NeededSmall$18,0002,4001Large$45,0006,0003

We will construct a linear programming problem according to the given conditions and solve it using…

Answered: i. formulate the LP Model; ii. identify…

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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Cecille Paper Company uses softwood and hardwood pulp as basic materials for producing converter-grade paper. Hardwood is 80% pulp fiber and 20% pulp binder, while softwood is 50% pulp fiber and 50% pulp binder. The cost per pound for hardwood and softwood is $.50 and $.40, respectively. The company s quality control expert specifies that in order for the product to meet quality standards, each batch must contain at least 12,000 pounds of pulp fiber and at least 6,000 pounds of pulp binder. Because of equipment limitations, the size of a batch cannot exceed 24,000 pounds. The Production Department recently received a new standard from the Cost Department, allowing $8,200 per batch. The production manager feels that this amount is too low, because such costs have never been less than $8,400. Required: Using the graphic method, determine the hardwood and softwood mix necessary to minimize the cost per batch.
Espresso Express operates a number of espresso coffee stands in busy suburban malls. The fixed weekly expense of a coffee stand is $1,400 and the variable cost per cup of coffee served is $0.61. Required: 1. Fill in the following table with your estimates of the company's total cost and average cost per cup of coffee at the indicated levels of activity. 2. Does the average cost per cup of coffee served increase, decrease, or remain the same as the number of cups of coffee served in a week increases?
Ethan Steel, Inc. has three factories that manufacture steel components for three different rail projects located at three different sites. They want to determine how many steel components must be transported from each factory to each project site. The demand for the steel components for the three projects, A, B and C, are 2500, 3000 and 4500, respectively. The production and shipping details are as below: Production details: Factory Maximum capacity 1 3000 5000 3000 2 3 Shipping details (with per-unit shipping cost in dollars): Project Factory A B C 1 7 8 2 2 6 5 4 3 1 9 6 Develop a linear programming optimization model to determine the distribution plan (from factories to projects) that minimizes the total transportation cost. (Do NOT solve the model.)
4. Suppose the cost function for machine A has the following characteristics: a. it is linear, b. when the machine is not producing parts the cost is $200, c. cost of producing each part is $4 (i.e., variable cost is $4 per part). Suppose the cost function for machine B has the following characteristics: a. it is linear, b. when the machine is not producing parts the cost is $270, c. cost of producing each part is $3 (i.e., variable cost is $3 per part). A. Find the cost equations for machine A; place in function form. Define your variables B. Find the cost equations for machine B; place in function form. Define your variables (use variables that are different than variables used in Part A) C. Determine the break even point. (Determine this algebraically, not graphically; be sure to show your work.) D. Provide a graph of these two cost functions. Label the 1. Axes, 2. Break even point as an ordered pair, and 3. The two functions. E. To minimize cost, what production…
Heinrich is a manufacturing engineer with the Miller Company. He has determined the costs of producing a new product to be as follows: Equipment cost: $288,000/year Equipment salvage value at EOY5 = $41,000 Variable cost per unit of production: $14.55 Overhead cost per year: $48,300 If the Miller Company uses a 5-year planning hori- zon and the product can be sold for a unit price of $39.75, how many units must be produced and sold each year to break even? Contributed by Paul R. McCright, University of South Florida
Suppose that a company needs 1,500,000 items during a year and that preparation for each production run costs $900. Suppose also that it costs $14 to produce each item and $3 per year to store an item. Use the inventory cost model to find the number of items in each production run so that the total costs of production and storage are minimized.
General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed as the table below. where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars. 1. Determine how to minimize the cost of meeting demands in Houston and Tampa. 2. Modify the answer to part a if no shipments through Atlanta are allowed. From LA Detroit Atlanta Houston Tampa To LA Detroit $97 $94 $87 $129 $147 $100 $103 $145 Atlanta Houston $95 $125 $103 $110 $95 $88 $60 $103 Tampa $156 $148 $56 $100

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