LP formulation:

Suppose that,

a_t= Number of robots available during quarter t.

b_t= Number of robots bought during quarter t.

s_t= Number of robots sold during quarter t.

i_t= Number of cars available during quarter t.

c_t= Number of cars produced during quarter t.

it'= Blockage demand for cars at the end of quarter t.

z= Cost of the company.

The cost of purchasing a robot is $5,000 and maintenance cost of a robot is $500

The selling cost of a robot at the beginning of each quarter is $3,000.

Holding cost of a car at the end of each quarter is $200.

For the backlog demand, the holding cost of a car at the end of each quarter is $300.

Therefore, it is necessary to minimize the cost of company

z= 500∑t=14at+200∑t=14it+5000∑t=14bt−3000∑t=14st+300∑t=14it'

The demand to be met for quarter 1 is 600. Therefore,

i1=i1'+c1−600

The demand to be met for quarter 2 is 800. Therefore,

i2=i2'+i1−i1'+c2−800

The demand to be met for quarter 3 is 500

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Chapter 4, Problem 24RP

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