23. F(s) = 5s² + 34s + 53 (s+3)²(s+1)
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- n the previousyear, at Hub Motors ltd, for a particular model of Mercedes, Nissanand Ford,one could purchase(in millionshillings)all three cars for a total ofKsh 150. This year, due to inflation, the same cars would cost Ksh 161. The cost of theMercedesincreased by 8%, the Nissan by 6%, and the Fordby 12%. If the price of last year’s Nissanwas Ksh 7less than the price of last year’s Mercedes, Use matrix inverse to findthe price of each of the three cars last yearThe manager of the Fore and Aft Marina in the previous problem wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 5 boats per hour and that the service rate for each server is 10 boats per hour. What is the average time a boat will spend waiting for service? What is the average time a boat will spend at the dock? If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing Why or why not?You are considering opening a book store near the campus, and you have begun an analysis of the situation. There are three possible sites under consideration. One is relatively small, the second is of medium size, while the third is large. If you open at site 1 and demand is good, you will generate a profit of $ 18,000. If demand is moderate, your profit is $12000 while with low demand, you will lose $ 6,000. If you open at site 2 and demand is high you will generate a profit of $ 28,000, if demand is moderate you will generate a profit of $1400 but you will lose $11,000 if the demand is low. If you open at site 3 and demand is high you will generate a profit of $ 42,000, if demand is moderate, you will generate a loss of $5000 and you will lose $18,000 if the demand is low You also have the option of not opening either. You believe that there is a 45% chance that the demand will be high, 25% chance that demand will be moderate. A market research study will cost $ 7,000. The…
- Products A and B requires various times for operations on machine M1, M2 and M3. During a certain productionperiod, M1 has 4000 minutes of time available, M2 has 6000 minutes , and M3 has 3000 minutes. Machine timeper unit of A 1 minute on M1, 2 minutes on M2 and no time on M3. Machine time per unit of B is 1 minute oneach of the three machines. Expected profit contributions are TK 60 per unit of A made and TK 75 per unit ofB. If production during the period is limited to products A and B, how many units of each should be made tomaximize the profit.a company manufactures two products x1 and x2 on three machines a, b, and c. X1 requires 1 hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of Rs.5/-. In the coming planning period the available time of three machines A, B, C are 2000 hours, 1500 hours, and 600 hours respectively. Find the optimal product mix.The annual sales of Crimson Pharmacy are expected to be given by S = 2.2 + 0.5t million dollars t years from now, whereas the annual sales of Cambridge Pharmacy are expected to be given by S = 1.3 + 0.7t million dollars t years from now. When will Cambridge's annual sales first surpass Crimson's annual sales?
- Where does the s+4 come from on step 2 (line 6)solve the seed value problem xy '' - y = 0 , y(2)=0, y'(2)=3Consider the following system of tanks. Each tank initially contains V1 = 200 gallons and V2 = 300 gallons of fresh water. At time t = 0 minutes, all three valves open up, allowing for a salt brine solution (at a concentration of 2 lbs/gal) to enter the first tank through the first valve. At the same time, the solution is allowed to pass from the first tank into the second tank, and finally, the solution is allowed to exit the second tank, all at the same rate of r = 5 gal/min. (a) Set up a system of differential equations that will allow you to solve for q1(t) and q2(t), which represent the amount of salt (in pounds) in tank 1 and tank 2, respectively, at time t. (b) Solve your system to find q1(t) and q2(t), and then graph them
- I only need question 4, Thank you. In the presence of enough food and lacking predators and competitors, a population of rabbitswill increase by a fixed percentage each spring. For this set of exercises, we will say that therabbit population increases by 10% each year. Thus, if the initial population is R0, then thepopulation the following spring will be R1 = (1.1)R0 rabbits. In two years, the population will beR2 = (1.1)R1 = (1.1)2R0. The number of rabbits after n years will beRn = (1.1)nR0,and clearly the rabbit population grows without bound. We will assume that the rabbit populationis measured in hundreds of rabbits (so that R = 1 represents 100 rabbits).Suppose now that we introduce a small number of cougars into the environment to keep the rabbitpopulation under control.Let’s suppose that the amount of rabbits eaten each year is proportional to the cougar population.Then the change in the rabbit population is governed by the equationRn+1 = (1.1)Rn − (0.1)Cn,where Rn and Cn…Jorge has decided to invest at most $80,000 in securities in the form of corporate stocks. He has classified his options into three groups of stocks: bluechip stocks that he assumes will yield a 10% return (dividends and capital appreciation) within a year, growth stocks that he assumes will yield a 15% return within a year, and speculative stocks that he assumes will yield a 20% return (mainly due to capital appreciation) within a year. Because of the relative risks involved in his investment, Jorge has further decided that no more than 30% of his investment should be in growth and speculative stocks and at least 50% of his investment should be in blue-chip and speculative stocks. Determine how much Jorge should invest in each group of stocks in the hope of maximizing the return on his investments. bluechip $ growth $ speculative $ What is the maximum return?3. Azonic, Ltd., a clothing firm, has fixed costs of $10,000 per year. These costs, such asrent, maintenance, and so on, must be paid no matter how much the company produces.To produce x units of a certain kind of suit, it costs $20 per suit (unit) in addition to thefixed costs. That is, the variable costs for producing x of these suits are dollars. Thesecosts are due to the amount produced and stem from items such as material, wages, fuel,and so on. The total cost C(x) of producing x suits in a year is given by a function C:C(x ) = (Variable costs) + (Fixed costs) = 20x + 10,000. a) Graph the variable-cost, the fixed-cost, and the total-cost functions.b) What is the total cost of producing 100 suits? 400 suits?