Apply the system of linear equations to solve the problem: One day in the morning, a vegetable seller named Ryen sold 20 potatoes to one of his customers and 10 tomatoes to another customer for a total of 175 taka. The following day, Ryen sold a total of 17 potatoes and 22 tomatoes for a total of 200 taka. It is given that, the prices of the vegetables is unchanged on both the days, what was the price of per unit of potato and tomato? #write your code here
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- You wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.A company produces two products on two machines. A unit of product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a unit requires 1 hour on machine 1 and 2 hours on machine 2. The revenues per unit of products 1 and 2 are $2 and $3, respectively. The total daily processing time available for machine 1 and 2 are 4 and 5 hours respectively. Letting and represent the daily number of units of products 1 and 2 respectively, (i)Construct the LP model to maximize profit. Obtain the optimum solution graphically by determining the number of units of each product to be produced in order to maximize the profit and at what value. If management decides to increase the daily capacity of machine 1 from 4 hours to 5 hours, locate the new optimum point. Compute and comment on the dual price and the feasibility range for machine 1.…A person places $5000 in an account that accrues interest compounded continuously. Assuming no additional deposits or withdrawals, how much will be in the account after seven years if the interest rate is a constant 8.5 percent for the first four years and a constant 9.25 percent for the last three years?
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