The AB manufacturing company has two kinds of products: A and B. They carn $180 profit for each Product A and $90 profit for each Product B. To produce Products A and B, the company needs three resources: Q, R, S. Each unit of Product A consumes 6 units of Resource Q and 2 units of Resource R. Each unit of Product B consumes 8 units of Resource Q and 3 units of Resource S. The AB manufacturing company only can use 48 units of Q, 12 units of R and 12 units of S per day, Resource Product A Product B Resource Available Q 8. 48 R 12 3. 12 Profit per unit 180 90 1. (30 points) Formulate a linear program and use simplex algorithm to solve it. 2. (20 points) Write down a linear programming model to determine the minimum total amount the insurance company should pay to AB manufacturing when they lose all the available resource. (Hint: consider the LP duality).