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Petroleum Production Wildcat Oil Company has two refineries, one located in Houston and the other in Tulsa. The Houston refinery ships
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Finite Mathematics for the Managerial, Life, and Social Sciences
- Solve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.arrow_forwardGold used to make jewelry is often a blend of gold, silver, and copper. Consider three alloys of these metals. The first alloy is 75% gold, 5% silver, and 20% copper. The second alloy is 75% gold, 12.5% silver, and 12.5% copper. The third alloy is 37.5% gold and 62.5% silver. If 100 g of the first alloy costs $2340.80, 100 g of the second alloy costs $2363.00, and 100 g of the third alloy costs $1350.00, how much does each metal cost? Gold costs $___/g (Round to the nearest cent as needed.arrow_forwardAssume that the production of 1 unit of magnesium requires 0.8 units of magnesium and 0.2 units of aluminum, and that the production of 1 unit of aluminum requires 0.3 units of magnesium and 0.2 units of aluminum.arrow_forward
- A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbo- hydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two slices of whole-grain bread supply 2.2 mg of iron, 10 g of protein, and 12 g of carbohydrates. Eiley is on a special diet which requires her to get 26.4 mg of iron, 160.5 g of protein, and 149 g of carbohydrates. (a) Write a system of linear equations that determines how many glasses of skim,how many quarter-pound servings of meat, and home many two-slice servings of bread she will need in her special diet. (b) Write the augmented matrix for your system, and use technology to obtain its re- duced row echelon form. (c) Use the result inpart(b)to determine how many glasses of skim,how manyq uarter- pound servings of meat, and home many two-slice servings of bread she will need in her special diet.arrow_forwardA factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 7,080 and 8,120. The time requirements and profit per unit for each product are listed below.arrow_forwardA dietician works in a hospital and prepares meals under the guidance of a physician. Suppose that for a particular patient, a physician prescribes a meal to have 850 calories, 55g of protein, and 140 mg of vitamin C. The dietician decides to prepare the meal using steak (each 3-oz serving contains 300 cal, 20 g protein, and no vitamin C.), bakes potatoes (one baked potato contains 100 Cal, 5g of protein, and 20 mg of vitamin C.), and Brussels Sprouts (one 156 g serving contains 50 Cal, 5 g of protein, and 100 mg of vitamin C). How many servings of each food are requried to satify the physician's requirements?____serving(s) of steak, _____ bakes potato(es), and ____ serving(s) of Brussels sprouts are required.arrow_forward
- Consider two interconnected tanks. Tank 1 initially contains 26 gal of water and 33 oz of salt, and Tank 2 initially contains 24 gal of water and 17 oz of salt. Water containing 2 oz/gal of salt flows into Tank 1 at a rate of 1 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 4 gal/min. Water containing 2.5 oz/gal of salt also flows into Tank 2 at a rate of 5.5 gal/min (from the outside). The mixture drains from Tank 2 at a rate of 9.5 gal/min, of which some flows back into Tank 1 at a rate of 3 gal/min, while the remainder leaves the system. (a) Let A(t) and B(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions that model the flow process. Observe that the system of differential equations is nonhomogeneous. A(0) B(0) = (b) Find the values of A(t) and B(t) for which the system is in equilibrium, that is, does not change with time. Let AE and BE be the equilibrium values. BE. %3D (c) Let a(t) = A(t) – A…arrow_forwardBecause of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 40 grams of sulfur dioxide and 120 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 40 grams of particulate matter for each gallon produced. The company makes a profit of 80¢ per gallon and 20¢ per gallon on the old and new processes, respectively. Answer parts (A) through (C) below. (A) If the government allows the plant to emit no more than 36,000 grams of sulfur dioxide and 90,000 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? Wha is the maximum daily profit? Summarize the model, Maximize Objective function subject to V 36,000 Sulfur dioxide constraint V 90,000 Particulate constraint х, у 2…arrow_forwardA diesel engine uses type A filter and high-grade lubricating oil costing P55 per liter. With this filter, the oil and the filter have to be changed every 500hrs. of operation, and 5L of oil have to be added every 100hrs. This filter costs P1480 a piece. Eighty liters of oil fill the engine. Another type, filter B, costing of P1200 may be used with a lower grade of oil costing P48 per liter. However, if this filter is used, the oil and filter have to be changed every 300hrs and 10 liters are added after each 150hrs the engine is used. Hint: Consider the cost per hour.arrow_forward
- A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 80 hrs of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.arrow_forwardThe number of collection vehicles a community would need for solid waste collection in a certain municipality is 6 trucks. Find a total number of services (customers) that are to be collected once per week during 4 working days. (Realistically, most trucks can service only about 200 to 300 customers before the truck is full and a trip to the landfill is necessary).arrow_forwardA furniture company makes dining room furniture. A buffet requires 30 hours for construction and 10 hours for finishing. A chair requires 20 hours for construction and 20 hours for finishing. A table requires 20 hours for construction and 60 hours for finishing. The construction department has 390 hours of labor and the finishing department has 210 hours of labor available each week. How many pieces of each type of furniture should be produced each week if the factory is to run at full сарacity? How many pieces of each type of furniture should be produced each week? Either buffet(s), chair(s), and no tables or buffet(s), chair(s), and 1 table. (Type whole numbers.)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,