MR. DER MANUELIAN
Linear Programming Story Problems Day 1Name:Date:Hour:When solving linear programming problems, use the following procedure:Define the ____________________Write a ____________________ of ________________________________________ the systemFind the coordinates of the ____________________ of the ____________________ ____________________Write a ____________________ in terms of the variables to be maximized or minimizedSubstitute the coordinates of the vertices into the function and use the results to answer the question.Example 1. A toy manufacturer wants to minimize her cost for producing two lines of toy airplanes. Because of supply materials, no more than 40 Flying Bats can be built each day and no more than 60 Flying Falcons can be built each day. There are enough workers to build at least 70 toy airplanes each day. It costs $12 to manufacture a Flying Bat and $8 to build a Flying Falcon. What is the minimum cost each day?Example 2. Juan makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz of varnish. It takes 2 hours to assemble an oak clock, which takes 4 oz of varnish. Juan has 16 oz of varnish in stock and can work a maximum of 20 hours. If he makes $3 profit on each pine clock and $4 profit on each oak clock, how many of each type should he make to maximize profits?Homework: Answer the following questions using the 6-step process.1. A seafood restaurant owner orders at least 50 fish. He cannot use more than 30 amberjack or more than 35 flounder. Amberjack costs $4 each and flounder costs $3 each. How many of each fish should he use to minimize his cost?2. Kristin earns $7 per hour at a video store and $10 per hour at a landscaping company. She must work at least 4 hours per week at the video store, but the total number of hours she works at both jobs cannot be greater than 15. Determine Kristin’s maximum weekly earnings (before deductions).3. As a receptionist for a veterinarian, one of Kim’s tasks is to schedule appointments. She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The veterinarian cannot do more than 6 surgeries per day. The office has 7 hours available for appointments. If an office visit costs $55 and most surgeries cost $125, how can she maximize the income for the day? What is that income? ................
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