In November 2024
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Write and execute a MATLAB program to solve the following function by Bisection Method
f(c )= 9.8 * 68.1/c [1- e(-0.146813c) ] – 40. Search your answer between c values 12 to 16.Assume minimum error to be considered as 0.001.
2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices
Bob’s Bike Shop is considering three options for his facility next year. He can expand his current shop, move to a larger facility, or make no change. With a favourable market, the annual payoff would be $56000 if he expands, $70000 if he moves, and $30000 if he does nothing. With an average market, his payoff will be $21000, $35000, and $10000 respectively. With an unfavourable market, his payoff will be $-29000, $-45000, and $5000 respectively.
Find the negative roots of the equation x^3-2x+5=0, correct to 3 places of decimal by Newton raphson method
B. The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1000 for the production setup. The variable cost is $30 per pair, and each pair sells for $40.
a. Let x indicate the number of pairs of shoes produced. Develop a mathematical mode
for the total cost of producing repairs of shoes.
b. Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes.
c. What is the breakeven point?
The lifetimes of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer’s output
a. What is the mean of the sample mean life? (2 marks)
b. What is the variance of the sample mean? (2 marks)
c. What is the standard error of the sample mean? (2 marks)
d. What is the probability that, on average, those nine light bulbs have lives of fewer than 1,050 hours? (4 marks)
Pio and Sons Inc. Spends P40, 000 to prepare a bid on a construction project. If the contract is awarded, the estimated revenue will be P300, 000. If the contract is not awarded, the company has a penalty of P50, 000. There is 40% chance that the company will be awarded the contract. Find the EV.
Determine whether or not the following statements are proportions.if they are not explain why
A.there is an integer x such that X²=9
B.please solve the equation y=2x4
C.why do we have to study logic
D.5+5=15
E.it is not true that 1 is a prime number
a workshop contains fur persons available for work on the four jobs only one person can work or anyone job the following table shows the cost of assigning each person on each job the objective only one person can work n any one job the following table shows the cost of assigning person to jobs such the total assignment cst is minimum
NTJ Distributors Ltd has has an annual demand for an airport metal detector of 1400 units. The cost of a typical detector is $400. Carrying cost is estimated to be 20% of the unit cost and the ordering cost is $25 per order. If Tricia Joseph, the owner, orders in quantities of 300, he can get a 4% discount on the cost of the detectors. Should the company accept the discount?
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