Question

GCB Banks are constantly looking for ways to increase their profits while minimizing costs. One area that banks focus on is their product offerings, as different products require varying amounts of resources and labour. To optimize their operations, the banks can use linear programming to determine the optimal product mix that maximizes profits while staying within resource constraints. Consider a mid-sized bank like Baroda Bank, that offers four main products: personal loans, mortgages, Debit cards, and car loans. Each product has specific requirements in terms of resources, such as personnel, marketing, and loan officers. To maximize profits while managing resources effectively, the bank must find the right balance of product offerings. The bank has six resource constraints: personnel, marketing budget, loan officers, computer systems, office space, and loan capital. The amounts of each resource available are Personnel: 25 employees, Marketing budget: GHc25000, Loan officers: 25, Computer systems: 10, Office space: 350 square meters, Loan capital: GHc1.5 million. Baroda’s production requirements for each product are: Personal loans: 2 personnel, GHc800 marketing, 3 loan officer, 2 computer system, 15 square meters office space, GHc6,000 loan capital, and 5 hours of labour Mortgages: 3 personnel, GHc4,000 marketing, 2 loan officers, 1 computer systems, 35 square meters office space, GHc80,000 loan capital, and 4 hours of labour Debit cards: 3 personnel, GHc1,000 marketing, 1 loan officer, 4 computer system, 15 square meters office space, GH2,500 loan capital, and 2 hours of labour Car loans: 2 personnel, GHc2,000 marketing, 3 loan officers, 3 computer system, 25 square meters office space, GHc60,000 loan capital, and 4 hours of labour Baroda makes the following profits for each product: Personal loans: GHc600 Mortgages: GHc1,5000 Debit cards: GHc80 Car loans: GHc3,000 The bank wants to maximize its profits while staying within its resource constraints.

Model the entire problem with Microsoft Excel Solver and answer the following question.
All answers with decimals must be to 2 decimal places
a. Compute the objective function value. Blank 1. Fill in the blank, read surrounding text.
b. What is the optimal solution? Blank 2. Fill in the blank, read surrounding text. , Blank 3. Fill in the blank, read surrounding text. .
c. What is the reduced Cost value for Debit Cards. Blank 4. Fill in the blank, read surrounding text.
d. What should be the maximum profit value for car loans for the optimal solution to remain the same? Blank 5. Fill in the blank, read surrounding text.
e. State the binding constraints.

Answer 1

Linear programming in Excel can help Baroda Bank find the optimal product mix to maximize profits while adhering to resource constraints. The bank needs to calculate the objective function, determine the optimal solution, identify the reduced cost for debit cards, and figure out the maximum profit for car loans to maintain the existing optimal solution. Binding constraints are critical as they represent the resources that fully limit additional profit.

Step-by-step explanation:

To maximize profits with given constraints, Baroda Bank can utilize linear programming through tools like Microsoft Excel Solver. By inputting the resource constraints, production requirements, and profit margins for personal loans, mortgages, debit cards, and car loans, Solver can calculate the optimal product mix to maximize profits. This involves setting up a mathematical model reflecting the bank's situation where each decision variable represents the quantity of each banking product to offer.

The objective function for this problem would be the sum product of the quantities of the products and their respective profits. Constraints would include the limits on personnel, marketing budget, loan officers, computer systems, office space, and loan capital. By running the Solver, we get the values that would give the highest possible profit without breaching the constraints, known as the optimal solution. The reduced cost value for a product, such as debit cards, indicates how much the profit would change if the constraint is relaxed or tightened. Lastly, if we want to keep the optimal solution the same when changing the profit of one of the products, like car loans, we need to figure out the maximum profit value it can have without affecting the optimal mix.

The binding constraints are those constraints that are 'tight' or exactly met in the optimal solution. These constraints limit the bank from earning more profit because the resources are fully utilized.