please answer dis asap g-Aay 2017 5. You are the production manager overseeing t

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please answer dis asap

g-Aay 2017 5. You are the production manager overseeing three plants producing Li-ion batteries Thes are used in electric vehicles, and are made in three grades: light, medium and heavy. The unit profits, monthly demand and Li requirements per battery are given in the table below Product Unit profit (per Heavy $12 Light $7 Maximum demand (units/month) 7 000 9 000 4 000 Li requirements battery) (kg/battery) 200 150 100 Medium $10 here are three plants where the batteries are produced. The maximum assembly capacities for ny mix of battery grades are given below. The number of batteries that can be manufactured at a ite is limited by the amount of Li the site can produce. The maximum Li production of each site also given below Plant Location Assembly capacity Maximum Li production, ,sef (kg/month) 100 000 70 000 40 000 nm Quebec City 5 500 Toronto 7500 Seattle 2 200 sPo Write a mathematical programming formulation that allocates production of the three battery grades among the three locations to maximize total profit The company negotiates a large ongoing order from Edison Motors, for their new electric sedan. The vehicle uses only Heavy batteries, and they need 10 000 units per month. This demand must be met each month, or the customer will be lost Modify your formulation to achieve this. a. b.

Explanation / Answer

Part a:

Decision Variables

Hi

Units of heavy-grade batteries produced in plants i

Mi

Units of medium-grade batteries produced in plants i

Li

Units of Light-grade batteries produced in plants i

Where, i = 1, 2, and 3 for plants located at Quebee city, Toronto, and Seattle respectively

Objective Function:

Objective is to maximize the profit from producing all three types of batteries.

Max Z = $12(Hi) + $10(Mi) + $7(Li) +

Subject to:

Demand of Heavy batteries

Hi <= 7000 or H1 + H2 + H3 <= 7000

Demand of Medium batteries

Mi <= 9000 or M1 + M2 + M3 <= 9000

Demand of Low batteries

Li <= 4000 or L1 + L2 + L3 <= 4000

Assembly capacity of plant at Quebee City

H1 + M1 + L1 <= 5500

Assembly capacity of plant at Toronto

H2 + M2 + L2 <= 7500

Assembly capacity of plant at Seattle

H3 + M3 + L3 <= 2200

Maximum Li production of plant at Quebee City

200H1 + 150M1 + 100L1 <= 100,000

Maximum Li production of plant at Toronto

200H2 + 150M2 + 100L2 <= 70,000

Maximum Li production of plant at Seattle

200H3 + 150M3 + 100L3 <= 40,000

Non-negative constraint

Hi , Mi , Li >= 0

Part b.

Decision Variables

Hi

Units of heavy-grade batteries produced in plants i

Mi

Units of medium-grade batteries produced in plants i

Li

Units of Light-grade batteries produced in plants i

Where, i = 1, 2, and 3 for plants located at Quebee city, Toronto, and Seattle respectively

Objective Function:

Objective is to maximize the profit from producing all three types of batteries.

Max Z = $12(Hi) + $10(Mi) + $7(Li) +

Subject to: (the first constraint will be replaced by new constraint for heavy-grade batteries)

Minimum units of Heavy-grade batteries to be produced is 10,000 units.

Hi >= 10,000 or H1 + H2 + H3 >= 10,000

Demand of Medium batteries

Mi <= 9000 or M1 + M2 + M3 <= 9000

Demand of Low batteries

Li <= 4000 or L1 + L2 + L3 <= 4000

Assembly capacity of plant at Quebee City

H1 + M1 + L1 <= 5500

Assembly capacity of plant at Toronto

H2 + M2 + L2 <= 7500

Assembly capacity of plant at Seattle

H3 + M3 + L3 <= 2200

Maximum Li production of plant at Quebee City

200H1 + 150M1 + 100L1 <= 100,000

Maximum Li production of plant at Toronto

200H2 + 150M2 + 100L2 <= 70,000

Maximum Li production of plant at Seattle

200H3 + 150M3 + 100L3 <= 40,000

Non-negative constraint

Hi , Mi , Li >= 0

Decision Variables

Hi

Units of heavy-grade batteries produced in plants i

Mi

Units of medium-grade batteries produced in plants i

Li

Units of Light-grade batteries produced in plants i

Where, i = 1, 2, and 3 for plants located at Quebee city, Toronto, and Seattle respectively

Objective Function:

Objective is to maximize the profit from producing all three types of batteries.

Max Z = $12(Hi) + $10(Mi) + $7(Li) +

Subject to:

Demand of Heavy batteries

Hi <= 7000 or H1 + H2 + H3 <= 7000

Demand of Medium batteries

Mi <= 9000 or M1 + M2 + M3 <= 9000

Demand of Low batteries

Li <= 4000 or L1 + L2 + L3 <= 4000

Assembly capacity of plant at Quebee City

H1 + M1 + L1 <= 5500

Assembly capacity of plant at Toronto

H2 + M2 + L2 <= 7500

Assembly capacity of plant at Seattle

H3 + M3 + L3 <= 2200

Maximum Li production of plant at Quebee City

200H1 + 150M1 + 100L1 <= 100,000

Maximum Li production of plant at Toronto

200H2 + 150M2 + 100L2 <= 70,000

Maximum Li production of plant at Seattle

200H3 + 150M3 + 100L3 <= 40,000

Non-negative constraint

Hi , Mi , Li >= 0

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