Happy Kid Toy Company produces two types of toy cars, A and B. The company makes RM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4 hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5 hours to paint. It takes 2 hours to produce the parts of one unit of B, 1 hour to assemble and 2 hours to paint. Every month, 2000 hours are available for pruducing the parts, 1800 hvurs for assembling the parts and 1550 hours for painting the toy cars. The company wishes to determine the best possible combination of toy cars A and B to be produced monthly to maximise the total profit. (i) Formulate the above as a linear programming problem. (ii) Solve the problem graphically. Obtain the optimal product mix and calculate the maximum total profit. (iii) By how much could the unit profit of toy car B change before the optimal product mix could change?
Happy Kid Toy Company produces two types of toy cars, A and B. The company makes RM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4 hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5 hours to paint. It takes 2 hours to produce the parts of one unit of B, 1 hour to assemble and 2 hours to paint. Every month, 2000 hours are available for pruducing the parts, 1800 hvurs for assembling the parts and 1550 hours for painting the toy cars. The company wishes to determine the best possible combination of toy cars A and B to be produced monthly to maximise the total profit. (i) Formulate the above as a linear programming problem. (ii) Solve the problem graphically. Obtain the optimal product mix and calculate the maximum total profit. (iii) By how much could the unit profit of toy car B change before the optimal product mix could change?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 8T
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Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
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The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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Transcribed Image Text:Happy Kid Toy Company produces two types of toy cars, A and B. The company makes
RM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4
hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5 hours to paint. It
takes 2 hours to produce the parts of one unit of B, 1 hour to assemble and 2 hours to paint.
Every month, 2000 hours are available for pruducing the parts, 1800 hvurs for assembling the
parts and 1550 hours for painting the toy cars.
The company wishes to determine the best possible combination of toy cars A and B to be
produced monthly to maximise the total profit.
(i)
Formulate the above as a linear programming problem.
(ii)
Solve the problem graphically. Obtain the optimal product mix and calculate the
maximum total profit.
(iii)
By how much could the unit profit of toy car B change before the optimal product mix
could change?
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