Giapetto is thinking of buying a new cutting tool for $20 to make toy soldiers and a new clamping tool for $15 to make toy trains. If he does not buy a new tool, he can still make a toy using the older tool he already has. However, using an old cutting tool leads to 50% of the produced soldiers and using an old clamping tool leads to 20% of the produced trains to be defective. With a new tool, there is no defective production. Giapetto cannot sell any defective product. Weekly demands (must be met exactly without left- over inventory) and productions costs are as follows: 1. Soldiers 2. Trains Demand (units/week) 400 300 Production cost ($/unit) 7 17

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Giapetto is thinking of buying a new cutting tool for $20 to make toy soldiers and a new clamping tool for $15 to make toy trains. If
he does not buy a new tool, he can still make a toy using the older tool he already has. However, using an old cutting tool leads to
50% of the produced soldiers and using an old clamping tool leads to 20% of the produced trains to be defective. With a new tool,
there is no defective production. Giapetto cannot sell any defective product. Weekly demands (must be met exactly without left-
over inventory) and productions costs are as follows:
1. Soldiers 2. Trains
Demand (units/week)
Production cost ($/unit)
400
300
7
17
There are other details about the problem which will be added later. Giapetto started formulating a mathematical model
considering only the above description and defined the following decision variables:
• xi: Production quantity for type i toy, i = 1, 2 corresponding to soldiers and trains, respectively.
Considering the above problem description, you need to figure out the rest of the decision variables in the below formulation and
fill the boxes appropriately.
y1 +
y2 +
x1 +
x2 (Objective & Objective Function)
s.t.
(1-y1) +
(1-у2) +
x1 +
x2
400 (Soldier demand)
(1-y1) +
(1-у2) +
x1 +
x2
v 300 (Train demand)
у1, у2
(Sign/type restrictions)
х1, х2
(Sign/type restrictions)
Transcribed Image Text:Giapetto is thinking of buying a new cutting tool for $20 to make toy soldiers and a new clamping tool for $15 to make toy trains. If he does not buy a new tool, he can still make a toy using the older tool he already has. However, using an old cutting tool leads to 50% of the produced soldiers and using an old clamping tool leads to 20% of the produced trains to be defective. With a new tool, there is no defective production. Giapetto cannot sell any defective product. Weekly demands (must be met exactly without left- over inventory) and productions costs are as follows: 1. Soldiers 2. Trains Demand (units/week) Production cost ($/unit) 400 300 7 17 There are other details about the problem which will be added later. Giapetto started formulating a mathematical model considering only the above description and defined the following decision variables: • xi: Production quantity for type i toy, i = 1, 2 corresponding to soldiers and trains, respectively. Considering the above problem description, you need to figure out the rest of the decision variables in the below formulation and fill the boxes appropriately. y1 + y2 + x1 + x2 (Objective & Objective Function) s.t. (1-y1) + (1-у2) + x1 + x2 400 (Soldier demand) (1-y1) + (1-у2) + x1 + x2 v 300 (Train demand) у1, у2 (Sign/type restrictions) х1, х2 (Sign/type restrictions)
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