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QUESTION 1: 16 7. -1 5 has no inverse. (10 Marks) a. Find the value of m if the matrix 3 9 11 m m

QUESTION 1: 16 7. -1 5 has no inverse. (10 Marks) a. Find the value of m if the matrix 3 9 11 m m

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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ME QUESTION 1: [6 7 m. 5 has no inverse. (10 Marks) 9 11 -1 a. Find the value of m if the matrix m. b. A textile industry sells 3 brands: B1, B2 and B3 of yarn, each of which is a blend of cotton from Pakistan, Egypt and America in ratios of: 1:2:1, 2:1:1 and 2:0:2. If cost/kg of B1, B2 and B3 is dollar 40, 50 and 60 respectively. Required: Find the cost/kg for cotton of each country using matrix inversion method (10 Marks) QUESTION 2: a) Cost function and Revenue function of a certain manufacturing firm in Ruvuma, Tanzania is given as follows; Cost Function (C(x)) = 4X² + 2X + 100 and Revenue function (R(x)) = 16X2 - 26X + 400 Required: Find the following i) Marginal Cost- (4 Marks) ii) Marginal Average cost (4 Marks) iii) Profit function (4 Marks) iv) Value of output, which minimize cost (4 Marks) b) The marginal cost of production of a firm is given by C (x)=15+3x. The marginal He revenue is given by R (x)=18x+ 25 .The fixed cost is Tsh 120. Find the profit function (4 Marks) QUESTION 3: a) An accounting firm will need Tsh. 17,000 in 5 years to replace its computer system. What periodic deposits to a sinking fund paying quarterly interest at a 9% annual rate will achieve that goal? (8 Marks) b) Balimi buys a new car that sells for sh. 12,000,000. He agrees to pay for he car over 4 years by making 48 payments, one at the end of each month, at an interest rate of 10%, compounded monthly.
Transcribed Image Text:ME QUESTION 1: [6 7 m. 5 has no inverse. (10 Marks) 9 11 -1 a. Find the value of m if the matrix m. b. A textile industry sells 3 brands: B1, B2 and B3 of yarn, each of which is a blend of cotton from Pakistan, Egypt and America in ratios of: 1:2:1, 2:1:1 and 2:0:2. If cost/kg of B1, B2 and B3 is dollar 40, 50 and 60 respectively. Required: Find the cost/kg for cotton of each country using matrix inversion method (10 Marks) QUESTION 2: a) Cost function and Revenue function of a certain manufacturing firm in Ruvuma, Tanzania is given as follows; Cost Function (C(x)) = 4X² + 2X + 100 and Revenue function (R(x)) = 16X2 - 26X + 400 Required: Find the following i) Marginal Cost- (4 Marks) ii) Marginal Average cost (4 Marks) iii) Profit function (4 Marks) iv) Value of output, which minimize cost (4 Marks) b) The marginal cost of production of a firm is given by C (x)=15+3x. The marginal He revenue is given by R (x)=18x+ 25 .The fixed cost is Tsh 120. Find the profit function (4 Marks) QUESTION 3: a) An accounting firm will need Tsh. 17,000 in 5 years to replace its computer system. What periodic deposits to a sinking fund paying quarterly interest at a 9% annual rate will achieve that goal? (8 Marks) b) Balimi buys a new car that sells for sh. 12,000,000. He agrees to pay for he car over 4 years by making 48 payments, one at the end of each month, at an interest rate of 10%, compounded monthly.
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