A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, $2, and $3, respectively. Fixed costs are $18,000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and$7, respectively. Next year, a total of 11,000 units of all three products is to be produced and sold, and a total profit of $23,000 is to be realized. If total cost is to be $79,000, how many units of each of the products should be producednext year?units of product A,units of product B, andunits of product C should be produced.

An equation is a statement in which two algebraic expressions are equal. If the equation is of the…

Answered: A manufacturer produces three products,…

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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On average, 275 customers arrive per hour at a huge branch of a Bank. It takes an average of two minutes to serve each customer. It costs $15 per hour to keep a teller window open, and the bank estimates that it will lost $50 in future profits for each hour that a customer waits in line. How many teller windows should the Bank keep open? 11 12 13 14
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.00. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between and min. (Enter your answers from smallest to largest.)(b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing Type A souvenirs and Type B souvenirs, where ≤ k ≤ .(c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.)$
A company uses 5000 items per annum which has a price of $2 each. The ordering costs are $150 per order and holding costs are $1.50 per item per annum. The company is offered a 5% discount (discounted price is $1.90) for orders of 5000 and over. Order cost and holding cost remain at $150 per order and $1.50 respectively. Assuming that the company orders 5000 items per order, calculate the number of orders per annum, average stock, annual stock holding cost, annual order cost, annual inventory cost and the total annual cost of items and inventory.
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Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize P = 1.75x + 1.25y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
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A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 900 labor-hours of fabrication time and 700 labor-hours of assembly time available per week. The profit on each component, A, B, and C, is $7, $8, and $10, respectively. How many components of each type should the company manufacture each week in order to maximize its profit (assuming that all components manufactured can be sold)? What is the maximum profit? Let x₁, x2, and x3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem. Maximize P=[ subject to X1, X₂, X3 20 The company should manufacture (Simplify your answers.) Fabrication time restriction Assembly time restriction…
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