Banks in Ghana 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: $20$ employees, Marketing budget: GHc$50,000,$ Loan officers: $10,$ Computer systems: $5,$ Office space: $500$ square meters, Loan capital: GHc$5$ million. Baroda$$s production requirements for each product are: Personal loans: $1$ personnel, GHc$1,000$ marketing, $1$ loan officer, $1$ computer system, $20$ square meters office space, GHc$10,000$ loan capital, and $2$ hours of labour Mortgages: $2$ personnel, GHc$5,000$ marketing, $3$ loan officers, $2$ computer systems, $50$ square meters office space, GHc$100,000$ loan capital, and $4$ hours of labour Debit cards: $1$ personnel, GHc$2,000$ marketing, $2$ loan officers, $1$ computer system, $10$ square meters office space, GHc$5,000$ loan capital, and $1$ hour of labour Car loans: $1$ personnel, GHc$3,000$ marketing, $2$ loan officers, $1$ computer system, $15$ square meters office space, GHc$20,000$ loan capital, and $3$ hours of labour Baroda makes the following profits for each product: Personal loans: GHc$500$ Mortgages: GHc$2,000$ Debit cards: GHc$50$ Car loans: GHc$1,000$ The bank wants to maximize its profits while staying within its resource constraints.

All answers with decimals must be to $2$ decimal places

Model the entire problem with Microsoft Excel Solver and answer the following question.

a$.$ What are the coefficient for Mortgage and Debit Cards, respectively? Blank $1.$ Fill in the blank, read surrounding text. Blank $2.$ Fill in the blank, read surrounding text.

b$.$ State the optimal Solution values or value? Blank $3.$ Fill in the blank, read surrounding text.

c$.$ What is the Objective Function Value? Blank $4.$ Fill in the blank, read surrounding text.

d$.$ Identify all the Binding Constraints? Blank $5.$ Fill in the blank, read surrounding text.

e$.$ Is Loan Capital a binding constraints? Blank $6.$ Fill in the blank, read surrounding text.

f$.$ Compute the maximum profit for Mortgage? Blank $7.$ Fill in the blank, read surrounding text.

g$.$ Compute the minimum profit required for Car Loans? Blank $8.$ Fill in the blank, read surrounding text.

h$.$ What is the Shadow price value for the binding constraints? Blank $9.$ Fill in the blank, read surrounding text.

i$.$ From the sensitivity report, which resource$($s$)$ must receive additional inputs? Blank $10.$ Fill in the blank, read surrounding text.

j$.$ What should be the maximum unit profit for Personal Loans for the optimal solution to change?