B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ andM2. Each unit of type A requires 1 hour of processing by M₁ and 2 hours in M and eachunit type of type B requires 3 hours on M₁ and 1 hour on M₂. The profit on product A isP20 per unit and on product B is P30 per unit. If M₁ is available for 200 hours each monthand M₂ for 300 hours, how many units of each type can be manufactured in one month inorder to maximize the profits?Requirement:1) Formulate the linear programming model2) Solve the linear programming using the graphical method

According to given information- Machine Product A (x) Product B (y) Time M1 1 3 200 M2 2 1…

Answered: B. A firm manufactures 2 product, A and…

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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A company manufactures three types of leather belts, namely A B and C. The unit profits from these three varieties are 10, 5 and 7 respectivel Leather is sufficient for only S00 belts per day (all types together) Belt A requires thrice the time of belt B and belt C requires twice the time of B. If all the belts of type B are produced, a maximum of 1,000 belts per day can be produced. Belt A requires a fancy buckle and 150 such buckles per day are availlable. There are sufficient number of buckles for the other varieties. Determine using simplex method, how many belts of each type be produced to maximize the total profit.
A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company’s resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufacturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit.a) Formulate a linear programming model for this problem.
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. 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 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ 48 X and $ 96 X. (Enter your answers from smallest to largest.) (b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $196.80. $2 (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $1.50 (with the contribution to the profit of a Type A souvenir held at $1.00)? $168
A small paint company specializes in two types of exterior paint: latex and enamel paint. It requires 10 labor-hours per 100 liters of latex paint and 15 labor-hours per 100 liters of enamel paint. It is assumed that the company works only 40 hours per week, does not hire additional labor, and does not engage in overtime work. From 1 liter of latex paint, a profit of 5 units is obtained, while from 1 liter of enamel paint, a profit of 10 units is obtained. The owner of the company prioritizes the objectives in the following order: Avoiding overtime work Maintaining a weekly profit of at least 1000 units Producing a minimum of 700 liters of enamel paint each week to meet the demand of an existing customer Formulate the goal programming model for the company.
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. 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 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ and $ . (Enter your answers from smallest to largest.)(b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $208.80.$ (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $2.00 (with the contribution to the profit of a Type A souvenir held at $1.00)?$
A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 7 cost of $56,048 and a variable cost per unit of XL7510 equal to 214 + - dollars, where is the total number of XL7510s produced. 10 Suppose further that the selling price of this product is 1180 The -values of the break-even points are The maximum revenue is Form the profit function: P(x) = The maximum profit is The price that will maximize profit is 3 10 - dollars per unit of XL7510. dollars (round to the nearest cent) dollars (round to the nearest cent)
XYZ Corporation operates two plants, each of which has a capacity of 200 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 17 units per day while customer D has a demand of 349 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 25 19 12 14 Plant 2 15 21 23 20 How many units should XYZ ship from each plant to each customer?

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