Name CA K44-14". Block 3-4B: Linear Programming Homework 1. An electronics company makes two kinds of TV's: LCD and plasma. Let x be the number of LCD TV's and y be the number of plasma TV's made in a month. The company has enough equipment to make as many as 1 LCD TV's per month or 6 plasma TV's per month. It takes 2 worker-hours to make a LCD TV and 3 worker-hours to make a plasma TV. The company has up to 24 worker-hours of labor available each month. They make $75 profit on LCD TV's and $125 on plasma TV's. a) Write the objective function: b) Identify the variables and write 5 constraints. You may set up a table: po 4:- tc t c Z X E /. v4 r /es rp a z. z 6 s c) Graph the constraints for this system on large graph paper and label the vertices: 1..1) o o c) ) o (.1 ( (1: (..). e) Substitute vertices into objective function: V (. X Z) -..-- -7 K f 1 D S--- 2..- 1) ( i. ).-... I s 4 i o s--. '-p ( oe ) t + I ;-.) r - C.- c; - d - ----/ c T.? ( I / ).1 c. I (..) I (1 r * 3 *': -7 5 `:) 1-) 6 5 ) 7 c..: C7 I c--- pcl What combination of LCD and plasma TV's will maximize profit? What will be the monthly profit? c)`7 c d - 3 (o C)
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2. A painter has exactly 32 units of yellow dye and 54 units of blue dye. He plans to mix as many gallons as possible of Light Green and Dark Green. Each gallon of Light Green requires 4 units of yellow and 1 unit of blue. Each gallon of Dark Green requires 1 unit of yellow and 6 units of blue. A gallon of Light Green generates a profit of $1 and a gallon of Dark generates a profit of $15. How many gallons of each color of green should the painter mix to maximize profits? a) Write the objective function: b) Identify the variables and write 4 constraints. You may set up a table: C ( S c)((rje 7- e) P 1 t ( i -i. v.. -3-. / s. e. 5- '. c) Graph the constraints for this system on large graph paper and label the vertices: I 9 e) Substitute vertices into objective function: :5- f) How many gallonso:7v! color of green should the painter mix to maximize profits? What will be the profit? I ; e. y /t o AT a -fi leo (Ler k
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1( A-) 3. A landscaping contractor uses a combination of two brands of fertilizers each containing different amounts of phosphates and nitrates as shown in the table: Phoip a per Pae e Nitrate Content per Package 4 lbs 6 lbs 24 lbs 2 lbs 5 lbs 15 lbs A certain lawn requires a mixture of at least 24 lbs of phosphates and at least 15 lbs of nitrates. Let a = the number of packages of Brand _A A. and b = the number of pacicagesof13rarid B. Now if a package of Brand A costs $6.99 and a package of Brand B costs $17.99 how many packages of each would minimize the contractor's cost? a) Write an objective function: b) List 4 constraints: 99 + I7 > 6 o_ 4-5- L) >;- 4 c) Graph the feasible region on large graph paper and identify the vertices. Li ) t 11 ) d) Substitute vertices into objective function: '-- " c C A A-- / -71 / e) How many packages of each would minimize the contractor's cost? How much would it cost?
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4. Suppose your mom is shopping for groceries. From a nutrition table she has learned that one ounce of hamburger has 1 mg of iron 1 mg of Vitamin A and 4 g of protein. One medium potato has 2 mg of iron mg of Vitamin A and 3 g of protein. For dinner your mom wants you to have at least 8 mg of iron 3 mg of Vitamin A and 27 g of protein to meet your daily nutritional requirements. If one medium potato costs $.1 and one ounce of hamburger costs $.15 how many potatoes and what number of ounces of hamburger should your mother buy to minimize the grocery bill? X t/ o el. 1 a) Write an objective function: " - b) Create a table to organize the given information. i. -...:::4. Ha -{ i...2.--17.:l...t Iriin _ ti n J +/-1 / D > / 's titin. A > - reri. ii`-' c) Write a system of 5 constraints using the information in the table..--) -ea:pr. r -.....-...f... --.a 7 ;4 2 ( X "3 d) Graph the system of inequalities on large graph paper. Identify the vertices of the feasible region. e) Substitute vertices into objective function: /6 f) How many potatoes and what number of ounces of hamburger should your mother buy to minimize the grocery bill? 1 5-- 3 Ouf\ef 1 - Jr 3e_r el ti et( e.1 c 41. 11-9.9.`' p How much is the bill?
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