# Algebra and Trigonometry

Mathematics

## Quiz 9 :Systems of Equations and Inequalities

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Use the method of substitution to solve the system.
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B

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A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.1, and a regular notebook, which sells for$0.85. The production cost is $1.00 for each deluxe notebook and$0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 7,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?
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B

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Solve the system using the inverse method.
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A

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Solve the system.
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Solve the system using the inverse method.
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Find the inverse of the matrix if it exists.
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A manufacturer of cell phones makes a profit of $23 on a deluxe model and$31 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?
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Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.
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Use the method of substitution to solve the system.
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Find a system of inequalities for the graph shown.
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Use matrices to solve the system.
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Solve the system using the inverse method.
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Use the method of substitution to solve the system.
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Use matrices to solve the system.
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Solve the system using the inverse method.
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A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and$50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?
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Find the inverse of the matrix if it exists.
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Find the inverse of the matrix if it exists.
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