Question

In: Operations Management

The Monet Company produces four types of picture frames, which are labeled types 1, 2, 3,...

The Monet Company produces four types of picture frames, which are labeled types 1, 2, 3, and 4. The four types of frames differ in size, shape, and materials used. Each type requires a certain amount of skilled labor, metal, and glass. These requirements, along with the profit for each one are shown in the table below:

	Labor (hours)	Metal (ounces)	Glass (ounces)	profit
Frame 1	2	4	6	$6
Frame 2	1	2	2	$2
Frame 3	3	1	1	$4
Frame 4	2	2	2	$3

During the coming week Monet has 4000 hours of labor, 6000 ounces of metal, and 10,000 ounces of glass. Also, due to market constraints, it is impossible to sell more than 1000 type 1 frames, 2000 type 2 frames, 500 type 3 frames, and 1000 type 4 frames. The company wants to maximize profits.

Formulate a linear program to determine how many of each type of frame should Monet build. Include an objective function and all constraints.

Expert Solution

Let the no. of frame 1 be x, frame 2 be y, frame 3 be z and frame 4 be w

Total Profit = 6x + 2y + 4z + 3w

We have to maximize this profit

Hence, we get the objective function as:

Maximize Profit P = 6x + 2y + 4z + 3w

Subject to constraints:

2x + 1y + 3z + 2w <= 4000............Constraint for no. of labor hours available.

4x + 2y + 1z + 2w <= 6000.............Constraint for ounces of Metal available

6x + 2y + 1z + 2w <= 10,000...........Constraint for ounces of glass available

x <= 1000........................................Constraint for max. no. of type 1 frames which can be sold

y <= 2000........................................Constraint for max. no. of type 2 frames which can be sold

z <= 500..........................................Constraint for max. no. of type 3 frames which can be sold

w <= 1000......................................Constraint for max. no. of type 4 frames which can be sold

x, y, z, w >= 0..................................Non-negativity constraints as no. of frames cannot be negative

----------------------------------------------------------------------------------------------------------------------------------------------------

In case of any doubt, please ask through the comment section before Upvote/downvote.

keosha answered 6 months ago

A company produces gold picture frames. The cost per picture frame is: Materials &nbsp

A company produces gold picture frames. The cost per picture frame is: Materials $9 Packaging $1 Decorations on the frame $5 Shipping and handling $1.5 Each worker earns $30,000 annually in salary and benefits. The number of workers changes based on the level of production. This means this is a variable cost. The artist who creates the designs on the picture frames is paid $25,000 annually. Senior management are paid a total of $200,000 annually. Other annual costs are:...

CVD Sdn Bhd (CVDSB) is a company located at Kedah. The company produces picture frames. Traditionally,...

CVD Sdn Bhd (CVDSB) is a company located at Kedah. The company produces picture frames. Traditionally, all frames are hand-made, which require one hour of direct labor to finish producing one frame. With the increasing demand on their products, the company plans to switch their manufacturing layout to the automated production facility by installing a new automated production machine which will save the direct labor hour used by 25% per frame. The company plans to install a new machine on...

1. Types of Company training? 2. What is career planning all about? 3. Which are the...

1. Types of Company training? 2. What is career planning all about? 3. Which are the main components of an employee's job satisfaction?

1.Describe the two types of product classifications. 2.Define the four types of consumer products. 3.Define a...

1.Describe the two types of product classifications. 2.Define the four types of consumer products. 3.Define a product item, a product line, and a product mix. 4.Describe the two key reasons why a firm might make adjustments to a product item, product line, or product mix. 5.Define the four primary adjustments a firm might make when adjusting product items, product lines, or product mixes. -Principles of Marketing.

A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns...

A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns a profit of $3 per pound. Brand II earns a profit of $4 per pound, and Brand III earns a profit of $3 per pound. 1 pound of Brand I requires 3 pounds of raw material and takes 2 hours of labor to produce it. 1 pound of Brand II requires 4 pounds of raw material and takes 3 hours of labor to produce...

Create a picture that includes representations for each of these four processes: 1. redox chemistry 2....

Create a picture that includes representations for each of these four processes: 1. redox chemistry 2. Glycolysis 3. Fermentation 4. TCA/citric acid cycle You should show the connections between these topics. The molecular pathways do not need to show all details but should have the main inputs and outputs (products) clearly labeled.

Part I: Define the following concepts 1. Write four types of Qur’anic commentaries: 1. 2. 3....

Part I: Define the following concepts 1. Write four types of Qur’anic commentaries: 1. 2. 3. 4. Part II. Define the following concepts: 1. Nabi 2. Ummah 3. Araft 4. Mina 5. Rasul 6. Shari`ah Part III. Answer the following questions: 1. Who put the Quran together in its current format and when was it done? 2. How many chapters and verses does the Quran have? 3. The Quran can roughly be divided into four different genres. What are they?...

14. There are eight balls in an urn, three red labeled {1, 2, 3}, a blue...

14. There are eight balls in an urn, three red labeled {1, 2, 3}, a blue ball marked {4}, and four white balls marked {5, 6, 7, 8}. Given the following three events, tell whether each possible pair of events (A and B, A and C, and B and C) is independent, disjoint, or neither. A. A red ball is drawn. B. An even numbered ball is drawn. C. A white ball is drawn.

Q 3 Abdelaziz Company produces 3 types of products. During the year the joint costs of...

Q 3 Abdelaziz Company produces 3 types of products. During the year the joint costs of processing the 3 products were $350,000. Production and sales value information were as follows: Sales Value Product Units produced at Split-Off Separable Costs Selling Price Product A 400,000 $10 per unit $6.00 per unit $40 per unit Product B 300,000 $9 per unit $4.00 per unit $28per unit Product C 500,000 $6 per unit $3.00 per unit $18 per unit a. Allocate...

number 1. Iguana, Inc., manufactures bamboo picture frames that sell for $25 each. Each frame requires...

number 1. Iguana, Inc., manufactures bamboo picture frames that sell for $25 each. Each frame requires 4 linear feet of bamboo, which costs $2.00 per foot. Each frame takes approximately 30 minutes to build, and the labor rate averages $13 per hour. Iguana has the following inventory policies: Ending finished goods inventory should be 40 percent of next month’s sales. Ending raw materials inventory should be 30 percent of next month’s production. Expected unit sales (frames) for the upcoming months...