Shop A provides 2 hours of cake training, 4 hours of cupcake training and 2 hours of bread training. Shop B provides 6 hours of cake training, 3 hours of cupcake training and 4 hours of bread training. Shop C provides 10 hours of cake training, 9 hours of cupcake training and 11 hours of bread training. Trainers must devote a minimum of 10 hours and a maximum of 36 hours to cake training, a maximum of 24 hours to cupcake training and a minimum of 15 hours to bread training. Shop A costs $85, Shop B costs $145, and shop C costs $175. The head chief aims to maximise the cost while satisfying the requirements of the three trainings respectively. Construct a table showing: ● ● the number of the elements required for each item the amount of each element available or the minimum requirements of each element. State the objective function and determine the constraints for each element. Produce a labelled graph showing the feasible region. Find the optimal solution by considering the feasible points. Determine the wastage or oversupply of elements for the optimal solution.

Shop A provides 2 hours of cake training, 4 hours of cupcake training and 2 hours of bread training. Shop B provides 6 hours of cake training, 3 hours of cupcake training and 4 hours of bread training. Shop C provides 10 hours of cake training, 9 hours of cupcake training and 11 hours of bread training. Trainers must devote a minimum of 10 hours and a maximum of 36 hours to cake training, a maximum of 24 hours to cupcake training and a minimum of 15 hours to bread training. Shop A costs $85, Shop B costs $145, and shop C costs $175. The head chief aims to maximise the cost while satisfying the requirements of the three trainings respectively. Construct a table showing: ● ● the number of the elements required for each item the amount of each element available or the minimum requirements of each element. State the objective function and determine the constraints for each element. Produce a labelled graph showing the feasible region. Find the optimal solution by considering the feasible points. Determine the wastage or oversupply of elements for the optimal solution.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 8T

See similar textbooks

Similar questions

Given a system of equations, explain at least two different methods of solving that system.
Can a linear system of three equations have exactly two solutions? Explain why or why not
An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?
Can a system of linear equations have exactly two solutions? Explain why or why not.
A clothing manufacturer makes trousers, skirts, and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time, and 5 minutes of packaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time, and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time, and 6 minutes of packaging time.The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Crammer's ????, determine how many of each type of clothing should be made to use all available labour hours?
A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time,24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Kramers rule method, determine how many of each type of clothing should be made to use all available labour hours?
A furniture manufacturing firm makes sofas and chairs, each of which is available in several styles. Each sofa, regardless of style, requires eight hours in the upholstery shop and four hours in the carpentry shop and can be sold for a profit of $450. Each chair requires six hours in the upholstery shop and 3.5 hours in the carpentry shop and can be sold for a profit of$375. There are nine people working in the upholstery shop and five in the carpentry shop, each of whom can work no more than 40 hours per week. a. What is that maximum profit? b. How many sofas and how many chairs should the firm make each week to maximize its profit? c. Is there an extra time in the upholstery shop? If so, how much? d. Is there an extra time in the carpentry shop? If so, how much?
A shoe company manufactures two types of shoes: tennis and basketball. Each shoe requires the use of two operations, stitching and coloring, and there are at most 28 hours available each day for each operation. A pair of tennis shoes requires 2 hours of stitching and 2 hours of coloring, while a pair of basketball shoes needs 1 hour of stitching and 2 hours of coloring. Due to other restrictions, the company can make at most 183 pairs of shoes a day. Additionally, due to a sponsorship agreement, the company needs to produce at least 4 pairs of tennis shoes for each pair of basketball shoes. The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)