1. Gotham Lending makes auto loans, mortgage loans, home equity loans, and commercial loans. Any funds not invested in loans are invested in an interest-bearing savings account. The following table gives the company's rate of return and risk level for each type of loan. Risk Loan type Auto loan Mortgage loan Home equity loan Commercial loan Savings account Rate of return 7.75% 11.25% 14.25% 8.75% 2.45% Gotham wants to invest $68,000,000 in available funding so that: Yearly return is maximized At least $5,000,000 is available in the savings account for emergencies The average risk should not exceed 5 At least 40% of the loan money is Commercial a) Define appropriate decision variables (include units of measure) b) Write objective equation c) Write constraint equations 2. PLV Market is a local retail grocery. Customers' groceries are charged by a cashier and bagged in either plastic or paper bags. These bags are supplied by a manufacturer who prints "PLV Market" on each bag to customize them for the grocery. The grocery has a standing order for 100 bags a day, at least 20 of these bags must be paper. Other constraints the bag manufacturer faces are the printing capacity and assembly capacity for the bags, shown below: minutes/plastic bag minutes/paper bag capacity (minutes) printing 2 300 assembly 480 The bag manufacturer may choose how many paper and plastic bags to supply PLV Market in a way that meets these constraints and minimizes manufacturing cost. Currently those costs are 5 cents per plastic bag and 6 cents per paper bag. a) Define decision variables for the bag manufacturer's decision b) Write linear programming equations to represent the bag manufacturer's decision. c) Solve this problem graphically. d) What is the bag manufacturer's optimal decision