The Kelly Company is a producer of canned vegetables. The company’s food processing plants are located in Sacramento and Dallas. Distribution centers are located in Denver, Cincinnati, Phoenix, and Atlanta. The supply chain manager wants to minimize the cost of shipping the goods from the processing plants to the distribution centers. Relevant data are given below. Develop and solve a linear optimization model to minimize the cost of shipping while meeting capacity and demand requirements. Evaluate the sensitivity report and provide a full explanation and any recommendations to the supply chain manager.

Per Case Cost of Shipping
	Denver	Phoenix	Cincinnati	Atlanta
Sacremento	$1.75	$1.25	$3.25	$5.50
Dallas	$1.90	$1.35	$2.75	$2.55

Weekly Capacity (cases)
Sacremento	3,000
Dallas	5,000

Weekly Demand (cases)
Denver	1,200
Phoenix	1,000
Cincinnati	1,900
Atlanta	2,500

Xij as amount shipped from processing plant i to distribution center j

Mathematical Model:
 Min 1.75X₁₁ +1.25X₁₂ + 3.25X₁₃ + 5.50X₁₄ + 1.9X₂₁ + 1.35X₂₂ + 2.75X₂₃ + 2.55X₂₄

Constraints

X₁₁ + X₁₂ + X ₁₃ + X₁₄ ≤ 3000

X₂₁ + X₂₂ + X ₂₃ + X₂₄ ≤ 5000

weekly demand

X₁₁ + X₂₁ = 1200

X₁₂ + X₂₂ = 1000

X₁₃ + X₂₃ = 1900

X₁₄ + X₂₄ = 2500

X_ij ≥ 0