systems of linear inequalities with graphing

Anonymous
timer Asked: Aug 21st, 2014

Question Description

Linear Inequality.docx 

Answers for all parts, explanations where necessary. 

Name_____________________________ SYSTEMS OF LINEAR INEQUALITIES MATERIALS TI-84 Graphing Calculator PART 1 OFFICE MANAGER You manage the office for a veterinarian. As an office manager, one of your tasks is to schedule appointments. 1/3 hour is required for a routine office visit and 1 hour for a surgery. The office is open at least 5 hours a day but will not exceed 8 hours. The vet has decided that the number of routine visits should be at least 3 times as many as the number of surgeries. A. Assign variables to the unknown quantities and write a system of inequalities that model the given restrictions. (3 points) Let x = Let y = HINT there are 2 kinds of appointments (3 points)What are the least number of hours that can be scheduled? Write as an inequality in terms of x and y: Solve for y: Inequality 1: (3 points)What are the most number of hours that can be scheduled? Write as an inequality in terms of x and y: Solve for y: Inequality 2: (3 points)Is there any restriction to the number of routine visits to surgeries scheduled? Write as an inequality in terms of x and y: Solve for y: Inequality 3: (3 points)Apply any common sense restrictions (can x or y be negative?): Inequality 4: Inequality 5: SYSTEMS OF LINEAR INEQUALITIES - OFFICE MANAGER PART 2 B. Graph the system, indicating an appropriate window and scale. Shade the feasible region. (4 points) Use your TI-84 to get your feasible region. Sketch a copy of your feasible region below. Label the axis and show the scale: C. Determine the vertices of the polygonal feasible region. The vertices of the shaded feasible region can be found numerically (by using table values on the calculator if desired), algebraically (by solving for the intersections of pairs of lines), or graphically. An approach that takes advantage of the calculator’s capabilities is described below. Before we find the x & y intercepts graphically, let us note that it can be easily determined that the y-intercepts by putting 0 in for x in our boundary equations above. The x- intercepts can be found by putting 0 in for y. Find the x-intercepts and list them: Find the y-intercepts and list them: Label them clearly on the graph in Part B Next get the other vertices: ON TI-84: With your graph from above visible on your screen Use PoI-Trace Press ALPHA F3 Use the arrow button Move cursor to the next intersection. List the vertices. (4 points) Label them clearly on your graph in Part B (1 point) Pick a point in the feasible region (shaded region) and show that it satisfies all of the inequalities. Explain what that point represents. (3 points) LINEAR PROGRAMMING D. An office visit costs $50 and a surgery costs $160. Find a combination of office visits and surgeries that will maximize the income that the veterinarian receives in a day. (4 points) Write an equation that represents the cost R in terms of x and y Revenue Equation: R = To maximize (or minimize) a value in linear programming, one need only check the vertices of the polygonal feasible region. (1 point) List all vertices found in PART C: (4 points) Plug values into the Revenue Equation: (2 points) What is the maximum revenue you can obtain in a day? (2 points) How many routine visits and surgeries should be scheduled to maximize the revenue?

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