Linear Programming Model for Johnson Food Pte Ltd

Problem Introduction

Question 1Johnson Food Pte Ltd produces canned corn for the local and overseas markets. They have four raw corn suppliers as part of their strategy toreduce the risk of exposure to a single supplier. Each day, Supplier 1, 2, 3 and 4 can provide 140kg, 100kg, 80kg and 60kg of raw corn, respectively. The purchased raw corn can be shipped to any of the three processing plants to be cooked and canned. The processing capacity for Plant 1, Plant 2 and Plant 3 is 180kg, 140kg and 120kg per day, respectively. Due to recent landslide, it resulted in the following logistical situations: Supplier 3 can only ship to Plant 2 and Plant 3, while Supplier 4 can only ship to Plant 3. Supplier 4’s owner is a long-time family friend and there is an agreement that Johnson Food Pte Ltd will purchase all that Supplier 4 could provide (i.e. it will purchase exactly 60kg of raw corn from Supplier 4 every day).The canned corn will eventually be sent to three warehouses for further distribution to the local and overseas distributors. Warehouse 1 serves as the storage facility for the overseas market while Warehouse 2 and 3 serves as the storage facility for the local market. Based on projected demand, the amount of canned corn needed daily at Warehouse 1, 2 and 3 are at least 160kg, 100kg and 120kg, respectively.Table 1shows the transportation cost ($/kg) from each corn supplier to the processing plants:TAs the in-house analyst, you have been tasked by the Operations Manager to provide him with the necessary advice.

Develop a relevant Linear Programming (LP) model that represents the problem. Pleaseclearly statethe decision variables, objective and constraints. Please limit the answer to within one page(b)Solvethe LP model using Microsoft Excel. Please provide the Answer Report and the Sensitivity Report and state the assumptions you have made and presentthe relevant advice to the Operations Manager.(c)Describe a business problem that can be solved by using LP. Please explain why LP is suitable for solving theproblem.Please also provide any limitations to the use of LP, if any. You do notneed to solve it.