A local bakery produces two popular items weekly: chocolate cakes and apple pies. The profit for a chocolate cake is $30, and an apple pie is $20. Each product requires two types of labor: baking and decorating. The chocolate cake needs 2 hours of decorating and 1 hour of baking, while an apple pie takes 1 hour for baking and 1 hour for decorating. The bakery has 1000 hours weekly for decorating and 800 hours for baking. Due to market demand constraints, the bakery should not produce more than 400 chocolate cakes per week. Hence, the bakery needs to know the optimal number of chocolate cakes and apple pies to maximize its total profit. Formulate the optimization model for this problem (the decision variables, objective function, and constraints).

A local bakery produces two popular items weekly: chocolate cakes and apple pies. The profit for a chocolate cake is $30, and an apple pie is $20. Each product requires two types of labor: baking and decorating. The chocolate cake needs 2 hours of decorating and 1 hour of baking, while an apple pie takes 1 hour for baking and 1 hour for decorating. The bakery has 1000 hours weekly for decorating and 800 hours for baking. Due to market demand constraints, the bakery should not produce more than 400 chocolate cakes per week. Hence, the bakery needs to know the optimal number of chocolate cakes and apple pies to maximize its total profit. Formulate the optimization model for this problem (the decision variables, objective function, and constraints).

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

See similar textbooks

Similar questions

bama pie company's assembly line operations (the assembly line operates for six hundred minutes per day) comprise of eleven tasks, with the longest task time being 2.4 minutes and the shortest task time being 0.4 minutes; the sum of the task times is eighteen minutes. the firm is working on balancing its assembly line operations. the firm needs to produce 200 pies per day; to achieve this, the firm calculates the required cycle time as ---- minutes?
Two vital stages in a production process are assembly I and assembly II. The unit load for the assembly I stage is 7.0 ( 50% higher for high skill) minutes, while it is 10.0 (30 % higher for high skill) minutes for assembly II. There are 7 employees working in assembly I and 8 employees working in assembly II. 65% of low skill labor and 35% of high skill labor are required at both stages. . On average 18% of the operating time is wasted, what's the theoretical unit load for Assembly II? answer is 9.06 please explain
The senior management at Davis Watercraft would like to determine if it is possible to improve firm profitability by changing their existing product mix. Currently, the product mix is delermined by giving resource priority to the highest contribution margin watercrafts. Davis Watercraft always has a contingent of 10 workers on hand; each worker is paid $25 per hour. Overhead costs are $38,000 per week. The plant operates 18 hours per day and 6 days per week. Labor is considered a fixed expense because workers are paid for their time regardless of their utilization. The production manager has delermined that workstation 1 is the bottleneck. Delailed production information is provided below. Model A B Price $495 $345 $525 Material costs $45 $35 $115 Weekly demand Processing Time Station 1 Processing Time Station 2 Processing Time Station 3 Processing Time Station 4 100 75 40 60 30 60 10 60 20 30 40 a. Using the traditional method, which bases decisions solely on a product's contribution…
Steel City Juice is a local company that makes two kinds of juice: orange juice and apple juice.Demand for orange juice is 60 barrels/hr, while demand for apple juice is 40 barrels/hr. The company only has one machine to extract juice from raw fruit. The machine can extract orange juice at a speed of 150 barrels/hr, or apple juice at 120 barrels/hr. Switching from one type to the other requires 30 minutes cleanup time.Please provide a production schedule and an associated process flow diagram that (i) cycles repeatedly through the two kinds, (ii) meets the required demand, and (iii) minimizes the amount of inventory held. (Here it is assumed that the production machine runs 24 hours a day, 7 days a week ) and what is the maximum inventory level of orange juice?
A recurring maintenance job in a factory is being done by a three-man crew. Due to the nature of the job and space limitations, it was observed that two of the men were idle 37% of the time; one of the men was also idle an additional of the time, and at any given time only one man was required. The men were each paid P24.00 per hour. Each time the job was performed a set of tools and equipment with a value equivalent to P36.00 per hour was used. If the three-men crew could complete the work in 5 hours, which crew size would be the most economical
Formtech Inc. produces transformers. Each order is custom designed and manufactured for the customer. Each order goes through 3 phases: Transformer Design, which takes 4 weeks. Procurement, which has a lead time of 8 weeks. Assembly and Testing, which takes 4 weeks The design group can handle only 4 projects at any given time. The other groups are not capacity constrained. How much total work-in-process (number of projects started but not yet completed) does the company typically have? (Hint: Little's Law)
A company manufactures clay bricks in batches. A batch consists of 200 bricks. The manager reports that his weekly production target is 1500 bricks. Each brick has to be processed through 5 machines on average. It takes on average 30 minutes to set up the machines and the average operation time is 6 minutes. There are 10 machines in the plant. Calculate the manufacturing lead time if the average non-operation time is 2 hrs. Calculate the production rate and If the plant operates 70 hours per week, calculate the production capacity Calculate the Production Capacity if the machines are only available for 85% of the time. Will the manager be able to meet his production target? Justify your answer.
A computer recycler sells computer enclosures to a computer remanufacturer. To meet monthly expected demand, the remanufacturer needs 2.000 enclosures. The recycler utilizes a four-step disassembly process with scrap rates given as follows: d1=0.08, d2=0.05, d3=0.05, and d4=0.03. How many computers must be recycler receive each month in order to meet the remanufacturer’s demand?
Apples are prepared in a process with two resources. The first resource has a capacity of 2.1 apples per minute. The capacity of the second resource is 4.4 apples per minute. The first resource has 1 worker and the second resource has 4 workers. One additional worker is hired who is as productive as the current workers. What is the new capacity of this process? _____ apples per minute
Manufacturers Inc. (MI) currently has a labor force of 10, which can produce 600 units per period. The labor cost is now $5000 per period per employee. The company has a long-standing rule that does not allow it to make use of any overtime. In addition, the product cannot be subcontracted, due to the specialized nature of the machinery that MI uses to produce it. As a result, MI can only increase/decrease production by hiring or laying off employees. The cost is $10000 to hire or lay off an employee. Inventory carrying costs are $200 per unit for any unsold items at the end of the period. The inventory level at the beginning of period 1 is 400 units. The forecast demand is 700 in period 1,600 in period 2,450 in period 3, 250 in period 4,500 in period 5, and 550 in period 6. a.) Compute the costs of the Chase Demand Strategy. b.) Compute the costs of the Level Strategy c.) Compare the costs of the two strategies. Which one is superior?
Manufacturers Inc. (MI) currently has a labor force of 10, which can produce 600 units per period. The labor cost is now $5000 per period per employee. The company has a long-standing rule that does not allow it to make use of any overtime. In addition, the product cannot be subcontracted, due to the specialized nature of the machinery that MI uses to produce it. As a result, MI can only increase/decrease production by hiring or laying off employees. The cost is $10000 to hire or lay off an employee. Inventory carrying costs are $200 per unit for any unsold items at the end of the period. The inventory level at the beginning of period 1 is 400 units. The forecast demand is 700 in period 1,600 in period 2,450 in period 3, 250 in period 4,500 in period 5, and 550 in period 6. a.) Compute the costs of the Chase Demand Strategy.
On a typical Saturday, Red Lobster serves 1,000customers. The restaurant is open for 12 hours. On average,150 customers are present. How long does an averagecustomer spend in the restaurant?