1. A Company produces two types of products: Product A and Product B from two raw materials: R1 & R2. Product A requires 4 units of R1 and 8 units of R2, whereas product B requires 8 units of R1 and 6 units of R2. Raw materials are 320 and 480 units of R1 and R2 are available in stock. It is learnt from the market that the demand of product A is at least 20 units. Profit of product A is $20/unit and that of product B is $15/unit. Find the production combination to maximize profit. Also find the maximum profit.

2. A furniture manufacturer makes two types of furniture – chairs and sofas. The production of the sofas and chairs requires three operations – carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The profit per chair is $90 and the profit per sofa is $75. How many chairs and how many sofas should be produced each day to maximize the profit?

3. A company manufactures three-speed, and five-speed bicycles. Each bicycle passes through three departments; fabrication, painting & plating, and final assembly. The relevant manufacturing data are given in the table below.

Labor Hours per Bicycle Maximum Labor-Hours Available per DayThree-Speed Five-Speed

Fabrication 3 4 70Painting & Plating 5 3 80

Final Assembly 4 3 70Profit per bicycle $80 70

a. How many bicycles of each type should the company manufacture per day in order to maximize its profit? What is the maximum profit?

4. You are the decision maker of an electronic company that manufactures two radio models, each on a separate production line. The daily capacity of the first line is 60 radios and that of the second is 75 radios. Each unit of the first model uses 10 pieces of a certain electronic component, whereas each unit of the second model requires 8 pieces of the same component. The maximum daily availability of the special component is 800 pieces. The profit per unit of models 1 and 2 is $30 and $20, respectively. Determine the optimum daily production of each model so that the company can earn maximum profit.