Question

2. Priceler manufactures sedans and wagons. The number of vehicles that can be sold each of the next three months are listed to Table 1. Each sedan sells for $10000 and each wagon sells for $11000. It cost $7000 to produce a sedan and $8000 to produce a wagon. To hold a vehicle inventory for one month cost $160 per sedan and $210 per wagon. During each month, at most 1600 vehicles can be produced. Production line restrictions dictate that during month 1, at least two thirds of all cars produced must be sedans. At the beginning of the first month, 400 sedans and 300 wagons are available. Formulate an LP that can be used to maximize Pricesler's profit during the next three months. Sedans Wagons Month 1 1200 700 Month 2 1600 800 Month 3 1300 600

couks you please solve problem 2 ?
Thank you

Answer 1

Formulation:

Let

S_j = No. of sedans produced in Month-j
W_j = No. of wagons produced in Month-j
ES_j = Ending inventory of sedans in Month-j
EW_j = Ending inventory of wagons in Month-j; for j=1,2,3

Maximize Z = total profit

= (10000 - 7000) (S₁ + S₂ + S₃) + (11000 - 8000) (W₁ + W₂ + W₃) - 160 (ES₁ + ES₂ + ES₃) - 210 (EW₁ + EW₂ + EW₃)

= 3000 (S₁ + S₂ + S₃) + 3000 (W₁ + W₂ + W₃) - 160 (ES₁ + ES₂ + ES₃) - 210 (EW₁ + EW₂ + EW₃)

Subject to,

S_j + W_j <= 1600 for j=1,2,3

S₁ >= 2/3 (S₁ + W₁) or, (1/3) S₁ - (2/3) W₁ >= 0

400 + S₁ - ES₁ = 1200 or, S₁ - ES₁ = 800
ES₁ + S₂ - ES₂ = 1600
ES₂ + S₃ - ES₃ = 1300

300 + W₁ - EW₁ = 700 or, W₁ - EW₁ = 400
EW₁ + W₂ - EW₂ = 800
EW₂ + W₃ - EW₃ = 600

S_j, W_j, ES_j, EW_j >= 0 for j=1,2,3