Afurniture manufacturer makes 3 models of sola sets (model A, B and C) and eab midel comics in 2 types of leather (type land II) Model A requires 5 m² of materials and 10 hours to make Model Brequires 6m² of materials and 11 hours to make. Model C requires 8 m² of materials and 14 hours to make. For sofa set made of type I leather, materials cost 550 per m² and labour cost is 50 per hour For sofa set made of types II leather, materials cost $80 per m² and labour cost is $35 per hour (a) Write down two matrices such that their product under matrix multiplication gives the total cost of materials and labour for the production of each type of leather for each model of sofa set (b) Find the total material and labour cost for all models of sofa sets under each type of leather.
Answers
Step-by-step explanation:
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Answer:
So for this question, we have a table of difference desk models and the work that you have to put into manufacturer cuts in construction finishing. And we know that the company has assessment of ours for each type of step of stage. And we want to accounts how many of each desk we should be making. So if we let our variables be the different models say a secure fence. Model B is the office model. Nancy is very deluxe model, and we will make some equations out This so for cutting. We have 100 hours each week for cutting, so I work has to be 100. I have a Children's model. Takes two hours. The office three is it looks too. And the construction we have to Fay one for be on three, See? And we have 100 hours for this and for finishing. We have one, eh? One for bay hands to see. For this, we have 65 hours. Yes, So now we have our three equations, and when we saw this system, we will get the number of different models that were going to be producing. Now that's making augmented matrix to service. The difficult part is just passing the question and working out how to translate the information into these equations. From here on, it's quite standards. So I'm gonna let this be my room because it's got one here. This could be word suit on. This could be for three. Okay, so my first variable is going to be a We will have 1 to 2 second column. Could be bi one one three. See, it's going to be two three two ever written inside is 65 101 100. Okay. And that's straight in with some elimination. So things have minus two. Well are too. And minus 21 plus, uh, three to eliminate these two. So it's my real world is unchanged. My road suit is now zero minus one, minus one and minus. That's he answer. Three is zero one minus two minus 30. Okay, for my next step, I'm going to just eliminate this one hit. And Steven, I just stepped out my first ever. I'm just going to add word, too. Directory where? One still unchanged. Artoo is also entrenched. Hands were three zero zero minus three minus 60. Oh, yeah. So That's very easy gassing elimination. And I'm ready for back substitution. So for three is minus three C equals minus 60. So for Miss Aiken, C. C. Because 20 artsy is minus. B minus. C equals minus fancy. So be equals 10 and where one is a must be plus two c. He was 65 so a equals 15. So for miss, we have our losses were going to make 15 of the reference model 10 of the office model and 20 nobody looks small to use all the time available.
