(Modified from Problem 1 in Section 7.4 (Exercise in Outline 11)) Consider a company that carves wooden soldiers. The company specializes in two main types: Confederate and Union soldiers. The profit for each is $28 and $30, respectively. It requires 2 units of lumber and 4 hr of carpentry to complete a Confederate soldier. It requires 3 units of lumber and 3.5 hr of carpentry to complete a Union soldier. Each week the company has 100 units of lumber delivered. There are 120 hr of carpenter machine time available. Determine the number of each wooden soldier to produce to maximize weekly profits. (a) Solve the problem using graphical analysis (use geometric solutions) to maximize the profits. (b) Solve the problem using algebraic solutions to maximize the profits. (c) Solve the problem applying the Simplex Method to maximize the profits. (You are supposed to obtain the same maximum profits for all three cases in (a)-(c).)
(Modified from Problem 1 in Section 7.4 (Exercise in Outline 11)) Consider a company that carves wooden soldiers. The company specializes in two main types: Confederate and Union soldiers. The profit for each is $28 and $30, respectively. It requires 2 units of lumber and 4 hr of carpentry to complete a Confederate soldier. It requires 3 units of lumber and 3.5 hr of carpentry to complete a Union soldier. Each week the company has 100 units of lumber delivered. There are 120 hr of carpenter machine time available. Determine the number of each wooden soldier to produce to maximize weekly profits. (a) Solve the problem using graphical analysis (use geometric solutions) to maximize the profits. (b) Solve the problem using algebraic solutions to maximize the profits. (c) Solve the problem applying the Simplex Method to maximize the profits. (You are supposed to obtain the same maximum profits for all three cases in (a)-(c).)
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Transcribed Image Text:(Modified from Problem 1 in Section 7.4 (Exercise in Outline 11)) Consider a
company that carves wooden soldiers. The company specializes in two main
types: Confederate and Union soldiers. The profit for each is $28 and $30,
respectively. It requires 2 units of lumber and 4 hr of carpentry to complete
a Confederate soldier. It requires 3 units of lumber and 3.5 hr of carpentry
to complete a Union soldier. Each week the company has 100 units of lumber
delivered. There are 120 hr of carpenter machine time available. Determine the
number of each wooden soldier to produce to maximize weekly profits.
(a) Solve the problem using graphical analysis (use geometric solutions) to
maximize the profits.
(b) Solve the problem using algebraic solutions to maximize the profits.
(c) Solve the problem applying the Simplex Method to maximize the profits.
(You are supposed to obtain the same maximum profits for all three cases
in (a)-(c).)
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