A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine Iand 3 hr of time available on Machine II in each work shift.(a) How many units of each product should be produced in each shift to maximize the company's profit?The maximum is P =at (x, y) = ((b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution.scs(c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume.s (resource) s(d) Find the shadow price for the resource associated with the time constraint on Machine I.

Answered: Image /qna-images/answer/292a3f95-abf4-47e2-bf73-d613bdba0870.jpg

Answered: A company manufactures x units of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Q1) A company manufactures two products (pl and p2) on three machines (ml, m2 and m3). Each of the products must be processed on all three machines. One unit of pl requires 5h (hours) of processing time on ml, 4h of processing time on m2 and 3h processing time on m3. Machining times required by a unit production of p2 are 2h, 3h and 4h respectively. The machine capacities are 270h, 250h, and 200h per pieces respectively. The unit profits for the products are $100 and $60 respectively. Additionally the manufacturer wants to produce at least five pl for each p2. Suppose that the produced each product is sold. Formulate a Linear Programming (LP) Model to determine the number of pl and p2 that maximize the overall profit. (Define the decision variables. Write the objective function, and the constraints. Indicate sign restrictions. Do not try to solve the problem.)
A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the boors, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost por unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery noeds at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…
5) A factory owner has 100 employees that produce 6000 computers per day. For each additional employee that the owner highers, the average production per employee decreases by 8 computers. How many employees should the owner have in order to maximize production?
b) A company finds that it can sell out a certain product that it produces, at the rate of 7 2 Tk.2 per unit. It estimates the cost function of the product to be Tk. 1000 + for x units produced. Find the number of units produced that will maximize profit. What is the amount of this maximum profit? What would the profit if 6000 units are produced?
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars. Suppose x represents the number of tons produced daily of interior paints and y represents…
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)
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.
Q1) A retail. Store stocks two types of shirts A and B. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts of type B. The storage capacity, however, is limited to a maximum of 600 of both types combined. Type A shirt fetches a profit of SR 2/- per unit and type B a profit of SR. 5/- per unit. (a) Formulate a mathematical model of the problem.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS