Question

Solve a two-period storage problem in which production is 250 in the first period and 150 in the second, while demand in each period is 200-P1 and 220-P2, respectively. Assume storage cost is 5+0.1P1 for each unit stored. Make sure you find 1) both prices and 2) quantities sold in each period, and 3) the quantity stored.

Answer 1

Total Production - Productin . Productim Period 2 Total Production - 2 t 150 0 400 Total Production - Total Consumption - Consumption in period Consumtim in period + opad Total Consumption (200p,] + [220 - Pe] Total Consumption = 420 -P, -P2 Equating Total Production = Total consumption 400 = 420 - Pi-P2 P, = 20-P (1) # Price linkage equation of Period 1 & 2 Pire en Period 2 = (Poire in Storage/ (Period at I (Cast P = P + SC P = Pit Stolp, = (P = 1.181 + 5/2

Salving equation ① & ② P = 20-P2 - 0) P = 1.1 Pits (2) P = 1.1 (20-2) + S = 22 - 1.1 P₂ +5 2.1P = 27 - P2 = 12.85 Approx) = P,= 20-12.85 P = 7.15 Findind consumption in each period Now 9, = 220-P 2 - 220 - 12.85 q, = 200-P a = 200-7.15 2 = 192.85 9 = 207.15 Mase of Quantity Sold en Quantity Sold in t excess period 1 = 192.850 eccophy Period a = 150 case of a exces I Demord

The quantity Stooed il calcolated as follows Storage en Period 1 = Production - Consumption = 250 - 192.85 I 97.15 1 tve) Storage en period 2= Boduction - Consumption = 150 207.15 E157.15