a Chegg" service" A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 112 kilograms. A delivery of 2 large boxes and 12 small boxes has a total weight of 115 kilograms. How much does each type of box weigh.
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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- The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. DeeganIndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to thecar using existing holes in the car’s frame. Model DRW is a heavier roll bar that must bewelded to the car’s frame. Model DRB requires 20 pounds of a special high-alloy steel, 40minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 poundsof the high-alloy steel will be available next quarter. In addition, Deegan estimates that2000 hours of manufacturing time and 1600 hours of assembly time will be available nextquarter. The profit contributions are $200 per unit for…The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is a heavier roll bar that must be welded to the car’s frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 pounds of the high alloy steel will be available next quarter. In addition, Deegan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit for model DRB and $280 per unit for model DRW. The linear…“A car manufacturer produces two versions of its popular medium sized model: ahatchback aimed at the family market and a coupe designed to appeal to affluentsingle customers.Both are based on the same chassis and differ only in the body kit used to makeup the cars. They are both produced at the same factory.There are 125,000 hours of manpower and 25,000 basic half-chassis units (twoper vehicle) available each week. The hatchback takes 2.5 hours of assemblytime while a coupe takes 9.5 hours.At least 1,300 hatchback models should be produced per week.Production is also constrained by the fact that owing to problems with a supplieronly 40,000 lock units are available per week. A hatchback uses six of these lockunits while a coupe uses four.The profit to the factory on a hatchback model is estimated to be £4,600 while theprofit on a coupe is £6,400.The market demand for the cars is high. It is known that demand will exceedproduction for time to come so they should be able to sell whatever…
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- A Trucking Company has been tasked to transport relief aid to a refugee camp from the nearest port. It has been estimated that the refugee camp requires at least 130 kilolitres of potable water, at least 162 tonnes of foodstuff and at least 2210 litres of fuel. The trucking company has two types of vehicles to their disposal, Volvo and Mack. A Volvo truck can carry 5 kilolitres of potable water, 18 tonnes of foodstuff and 130 litres of fuel. A Mack truck can carry 13 kilolitres of potable water, 9 tonnes of foodstuff and 170 litres of fuel. It is estimated that a Volvo truck will take 32 hours for a round trip and a Mack vehicle will take 22 hours per round trip. If the Manager of the company wants to minimise the total number of truck hours taken to move the supplies, what mix of Volvo and Mack vehicles should he choose? Formulate this problem as a Linear Programming problem. Solve this Linear Programming problem using the Graphical approach. What is the optimal solution? Solve…a dietician wishes a patient to hav a meal that has 54 grams of protein, 84 grams of carbohydrates ann 380 miligrams of calcium. Today's diner is chicken, corn and milk. Chicken has 40 grams of proteuin, 45 grams of carbohydrats and 100 miligrams of calcium. Corn has 3 grams of protein, 14 grams of carbohydrates and 10 miligrams of calcium. Milk has 8 rams of protein , 11 grams of carbohydrates and 260 miligrams of calcium. How many servings of each food should she provide?A refinery has two smelters that extract metallic iron ore. Smelter A pro- cesses 1000 tons of iron ore per hour and uses 7 megawatts of energy per hour. Smelter B processes 2000 tons of iron ore per hour and uses 13 megawatts of energy per hour. Each refinery must be operated at least 8 hours per day and, of course, no more than 24 hours. If the refinery must process at least 30,000 tons of iron ore per day, how many hours should each smelter operate in order to expend as little energy as possible? (a) Set this up as a linear programming problem.(b) Solve the linear programming problem you wrote using the graphical method.