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- aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _With the extra profits generated from the new customers, Jacobi is considering expanding his product range. He is interested in stocking a new type of motorcycle headset camera. To fit with current business plans, the new product would have to generate a minimum of 37.5% margin to be worthwhile. With that in mind, he hypothesises that customers will be willing to pay at least $350 for this product, which is the minimum sale price for it to be viable at the specified margin. To test if his belief is true, Jacobi hires a market researcher (you) to determine how much customers may be willing to pay for this product. You collect data from a sample of 100 motorcycle enthusiasts, all of whom resemble Jacobi’s usual clientele, and determine that the average amount people are willing to pay is $364, with a standard deviation of $35.Using this information, you conduct a hypothesis test at a 5% level of significance to check whether Jacobi’s belief is justified and to help him decide whether to…4. An offshore oil well located at a point W that is 5 km from the closest point A on a straight shoreline. Oil is to be piped from W to a shore point B that is 8 km from A by piping it on a straight line underwater from W to some shore point P between A and B and then on to B via pipe along the shoreline. If the cost of laying pipe is P10,000,000/km underwater and P5,000,000/km over land, where should the point P be located to minimize the cost of laying the pipe?
- A food manufacturing company wants to hire an auditing firm to asses their food safety performance. Two auditing firms are considered: firm A will change 42$/hr and a flat fee of $4500, while firm B will charge 50$/hr with a flat fee of $3900. What is the break-even point in number of required auditing hours that would yield equal value from both companies?An electric company manufactures two different types of air conditions say, A and B. Both air conditions go through the first finisher and then the packer. Air condition A requires 2 hours of the finishing time and 1 hour of packing time. Air condition B requires 14 hours of finishing and 2 hours of packing time. The finisher has 10 hours, and packer has 8 hours of available time each month. Profit on one A air condition is 25 RO and on one B air condition is 15 RO Assuming that the company can sell all that produced. How many of each type of air condition should be manufacture to obtain the best return. (Use any method to find the best return)With the extra profits generated from the new customers, Jacobi is considering expanding his product range. He is interested in stocking a new type of motorcycle headset camera. To fit with current business plans, the new product would have to generate a minimum of 37.5% margin to be worthwhile. With that in mind, he hypothesizes that customers will be willing to pay at least $350 for this product, which is the minimum sale price for it to be viable at the specified margin. To test if his belief is true, Jacobi hires a market researcher (you) to determine how much customers may be willing to pay for this product. You collect data from a sample of 100 motorcycle enthusiasts, all of whom resemble Jacobi’s usual clientele, and determine that the average amount people are willing to pay is $364, with a standard deviation of $35. Using this information, you conduct a hypothesis test at a 5% level of significance to check whether Jacobi’s belief is justified and to help him decide whether to…
- 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 yearA baseball card store can obtain Mel Schlabotnic rookie cards at a cost of $4 per card. The store has been offering the cards at $13 apiece and, at this price, has been selling 28 cards per month. The store is planning to lower the price to stimulate sales and estimates that for each 50-cent reduction in the price, 4 more cards will be sold each month. At what price should the cards be sold to maximize total monthly profit?To minimize costs on the production line, an industrial engineer at a fiber-optic manufacturing firm is considering two robots. Robot X would have a $82,000 first cost, a $30,000 annual maintenance and operation (M&O) cost, and $50,000, $42,000, and $35,000 salvage prices after 1, 2, and 3 years, respectively. Robot Y will have a first cost of $97,000, a yearly M&O cost of $27,000, and after 1, 2, and 3 years, respectively, salvage prices of $60,000, $51,000, and $42,000. If a 2-year study period is specified at an interest rate of 15 percent per year and replacement after 1 year is not an option, what robot should be selected?
- A firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is x2 + 600 dollars and the cost of producing y units of the same product at plant Y is given by 3y2 + 1400 dollars. If the firm has an order for 2400 units, how many should it produce at each plant to fill this order and minimize the cost of production?In recent years, the United States and Japan have engaged in intense negotiations regarding restrictions on trade between the two countries. One of the claims made repeatedly by U.S. officials is that many Japanese manufacturers price their goods higher in Japan than in the United States, in effect subsidizing low prices in the United States by extremely high prices in Japan. According to the U.S. argument, Japan accomplishes this by keeping competitive U.S. goods from reaching the Japanese marketplace. Automobile Retail Prices (thousands of dollars) USA Sales: 18.2 16.2 17.2 18.7 18.4 16.6 14.9 16.8 12.1 10.8 18.5 15.5 16.2 16.3 18.2 19.5 13.2 16.8 12.9 17.2 18.2 16.3 16.8 16.4 18.6 15.6 17.1 18.1 18.9 19.0 17.3 18.8 14.9 16.7 20.3 17.1 14.6 17.2 13.0 18.4 16.9 13.3 16.3 15.9 16.6 17.6 16.0 17.1 14.6 18.0 Japan Sales:…In recent years, the United States and Japan have engaged in intense negotiations regarding restrictions on trade between the two countries. One of the claims made repeatedly by U.S. officials is that many Japanese manufacturers price their goods higher in Japan than in the United States, in effect subsidizing low prices in the United States by extremely high prices in Japan. According to the U.S. argument, Japan accomplishes this by keeping competitive U.S. goods from reaching the Japanese marketplace. Automobile Retail Prices (thousands of dollars) USA Sales: 18.2 16.2 17.2 18.7 18.4 16.6 14.9 16.8 12.1 10.8 18.5 15.5 16.2 16.3 18.2 19.5 13.2 16.8 12.9 17.2 18.2 16.3 16.8 16.4 18.6 15.6 17.1 18.1 18.9 19.0 17.3 18.8 14.9 16.7 20.3 17.1 14.6 17.2 13.0 18.4 16.9 13.3 16.3 15.9 16.6 17.6 16.0 17.1 14.6 18.0 Japan Sales:…