Question 1

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the constraint for resource III?

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Question 2

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the constraint for resource II?

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Question 3

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What are the corner points of the feasible solution space?

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Question 4

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
Is the production combination 15 A's and 15 B's feasible?

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Question 5

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the slack (unused amount) for each resource for the optimum production combination?

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Question 6

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the objective function?

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Question 7

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
Is the production combination 10 A's and 10 B's feasible?

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Question 8

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the optimum production combination and its profits?

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Question 9

Wood Specialties Company produces wall shelves, bookends, and shadow boxes. It is necessary to plan the production schedule for next week. The wall shelves, bookends, and shadow boxes are made of oak, of which the company has 600 board feet. A wall shelf requires 4 board feet, bookends require 2 board feet, and a shadow box requires 3 board feet. The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes, bookends require 15 minutes, and a shadow box requires 15 minutes. The power saw is expected to be available for 36 hours next week. After cutting, the pieces of work in process are hand finished in the finishing department, which consists of 4 skilled and experienced craftsmen, each of whom can complete any of the products. A wall shelf requires 60 minutes of finishing, bookends require 30 minutes, and a shadow box requires 90 minutes. The finishing department is expected to operate for 40 hours next week. Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95.
(A) Is this a problem in maximization or minimization?
(B) What are the decision variables? Suggest symbols for them.
(C) What is the objective function?
(D) What are the constraints?

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Question 10

A small firm makes three products, which all follow the same three-step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit.
Use the following computer output to find the optimum mix of products in terms of maximizing contributions to profits for the next period.
PROBLEM TITLE: LINEAR PROGRAMMING
PROBLEM IS A MAX WITH 3 VARIABLES AND 3 CONSTRAINTS. $$\begin{array} { | l | l | l | l | l | } 
\hline \text { ROW } & \text { X1 } & \text { X2 } & \text { X3 } & \text { RHS } \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | l | } 
\hline \text { COST } & 6.00 & 4.00 & 10.00 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | l | l | r | } 
\hline 1 - & 6.00 & 2.50 & 5.00 & \leq & 1,200.00 \
\hline 2 - & 5.00 & 2.00 & 4.00 & \leq & 900.00 \
\hline 3 - & 4.00 & 2.00 & 8.00 & \leq & 1,440.00 \
\hline
\end{array}$$ NUMBER OF ITERATIONS: 2
OPTIMAL SOLUTION:
OBJECTIVE FUNCTION VALUE = 2,070
DECISION VARIABLE SECTION: $$\begin{array} { | c | c | c | c | } 
\hline \text { VARIABLE } & \text { STATUS } & \text { VALUE } & \text { REDUCED COST } \
\hline \mathrm { X } 1 & \text { Non-basic } & 0 & 3.5 \
\hline \mathrm { X } 2 & \text { Basic } & 180 & 0 \
\hline \mathrm { X } 3 & \text { Basic } & 135 & 0 \
\hline
\end{array}$$ SLACK VARIABLES SECTION: $$\begin{array} { | c | c | c | c | } 
\hline \text { SLACK } & \text { STATUS } & \text { VALUE } & \text { SHADOW PRICE } \
\hline \mathrm { X } 4 & \text { Basic } & 75 & 0 \
\hline \mathrm { X5 } & \text { Non-basic } & 0 & 1.5 \
\hline \mathrm { X6 } & \text { Non-basic } & 0 & .5 \
\hline
\end{array}$$

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Question 11

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the constraint for resource I?

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Quiz 19: Linear Programming