Question

2. Due to the increasing demand for essential items, Quant Goods Company decided to increase the weekly production amounts. The local grocery stores reached out to the company to sign a short-term contract to receive these items from Quant Goods. They noted that the demand for toilet papers, hand sanitizers, chicken breast, and ground beef in three neighborhoods (neighborhood A, B, C) is significantly © N. Orkun Baycik, 2020 high. Due to production capacities, Quant Goods cannot supply for all three neighborhoods. Below are the details about the demand and production processes: • Quant Goods must produce at least 1000 rolls of toilet papers per week, at least 50 bottles of hand sanitizers, at least 125 pounds of chicken breast, and at least 150 pounds of ground beef for neighborhood A if they decide to sign a contract with this neighborhood. • Quant Goods must produce at least 1200 rolls of toilet papers per week, at least 100 bottles of hand sanitizers, at least 75 pounds of chicken breast, and at least 100 pounds of ground beef for neighborhood B if they decide to sign a contract with this neighborhood. • Quant Goods must produce at least 800 rolls of toilet papers per week, at least 80 bottles of hand sanitizers, at least 95 pounds of chicken breast, and at least 120 pounds of ground beef for neighborhood C if they decide to sign a contract with this neighborhood. • Quant Goods can produce at most 2500 rolls of toilet papers, 100 bottles of hand sanitizers, and 400 pounds of meat (chicken breast and ground beef in total) per week. • Producing each roll of toilet paper costs $0.5, each hand sanitizer bottle costs $0.65, and each pound of meat costs $0.70. Quant must decide which neighborhood stores to contract with and determine the production quantities while minimizing the total production costs and satisfying all the requirements listed above.

(a) Define your decision variables.

(b) Write the mathematical model that can be used to solve this problem (must provide the objective function and constraints mathematically). Note that simply providing the Excel solver input will not earn any credit.

Answer 1

							Quantity
Items	Units		Cost	Neighbourhood	Capacity
	A	B	C
Toilet Papers	Rolls	P	0.50	1,000	1,200	800	2,500
Hand Sanitizers	Bottles	Q	0.65	50	100	80	100
Chicken Breast	Pounds	R	0.70	125	75	95	400
Ground Beef	Pounds	S	0.70	150	100	120

Quant has to satisfy all the requirements of neighbourhoods if they take the contract

It can be seen from the above table that it cannot satisfy two neighbuorhoods at a time as capacity of handsanitizers is 100 bottles and AB, AC, BC, ABC combined together cannot fulfill demand of individual neighboorhoods at available capacity

Since there are capacity constraints to individual item, variables P, Q, R, S is assigned to items.

Ojective Function : Min Cost = 0.5P + 0.65Q+ 0.7R + 0.7Q (to be analysed for neighbourhood A,B, C individually)

Constraints: P <= 2500, Q <=100, R+S <=400