Objective To maximize profit

Profit Profit Alpha + Profit beta

sale of Product +

Assumtion is produced means sold

Production +

Explain in Mathematical form

Profit = A's Profit + B's profit= Pa*sa + Pb*Sb= Pa*Xa + Pb*Xb

Testing = 1*Xa + 1*Xb

<= 120

Assembling = 10*Xa + 15*Xb

<=2000

desktop Xa 120 Pa 350laptop Xb 0 Pb 470Workstation Xc 40 Pc 610

Aline 120Cline 40 Testing ALabour hours 2000 C

Labour hours

Shadow price With increase in 1 unit of labour hour how much my profit is increasing or decreasingHere it is 30.5 by changing labour hour to 2001 from 2000

If sharing is allowed I can give you A-line testing but you'll have to purchase 100 units

Upto 45 we are gettin

Maximize sale of Alpha

Maximize sale of beta

Maximize Production of Alpha

Maximize Production of beta

Part BTesting = 1*Xa + 1*Xb

<= 120

Assembling = 10*(Xa+Xa') + 15*Xb

<=2000

desktop Xa 120 Pa 350laptop Xb 0 Pb 470Workstation Xc 36 Pc 610desktop in Cline Xa' 8.0

Aline 120Cline 48Labour hou 2000

Part CTesting = 1*Xa + 1*Xb

<= 120

Assembling = 10*(Xa+Xa') + 15*Xb

<=2000

desktop Xa 121 Pa 350laptop Xb 0 Pb 470Workstation Xc 39.5 Pc 610

Aline 121Cline 39.5Labour hou 2000

+ Profit gamma

+

+

Pa Profitability of A 350Pb 470

+ C's Profit Pc 610+ Pc*Sc Sa No. of A Sold+ pc*Xc Xa No. of A produced

+ 1*Xc

<=48

+ 20*Xc

Profit 6640070030.5 3630.5

available used Left over120 120 0 Scarce profitability for scarce resorce should be prioratized

48 40 8 surplus

2000 2000 0 Scarce

With increase in 1 unit of labour hour how much my profit is increasing or decreasingHere it is 30.5 by changing labour hour to 2001 from 2000

I can give you A-line testing but you'll have to purchase 100 units

Maximize sale of Gamma

Maximize Production of gamma

+ 1*Xc+1.5*Xa'

<=48

+ 20*Xc

Profit 66760

+ 1*Xc+1.5*Xa'

<=48

+ 20*Xc

Profit 66445

With 1 unit increase in A line profit changes by 45

profitability for scarce resorce should be prioratized