Question: 1. A store sells men's tennis shoes. It makes a profit of $1 a pair on the men's shoes and $1.20 a pair on the ladies It takes two minutes of a sales person's time and two minutes of a cashier's time to sell a pair of men's shoes.It takes three minutes of a sales person's time and one minute of a cashier's time per pair of women's shoes. The store is open eight hours per day, during which time there are two salespersons and one cashier on duty. How much of the salesperson's and the cashier's time should be allocated to the men's and ladies shoes and how many shoes should the store sell to maximize profit?

2. Nitron Corp of Canada produces two products. Unit profit for product A is Tk. 60; for product B Tk. 50. Each must pass through two machines, P and Q. Product A requires 10 minutes on machine P and 8 minutes on machine Q. Product B requires 20 minutes on machine P and 5 minutes on machine Q. Machine P is available 200 minutes a day, while machine Q is available 80 minutes a day. The company must produce at least two units of product A and five of product B each day. What is the most profitable daily production plan? Solve graphically.

3. Copperfield Mining Company owns two mines, each of which produces three grades of ore-high, medium, and low. The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium grade ore and 24 tons of low grade ore. Each mine produces a certain amount of each type of ore during each hour that it operates. Mine 1 produces 6 tons of high grade ore, 2 tons of medium -grade ore, and 4 tons of low - grade ore per hour. Mine 2 produces 2, 2 and 12 tons, respectively, of high, medium and low grade ore per hour. It costs copper field $200 per hour to mine each ton of ore from mine 1, and it costs $160 per hour to mine each ton of ore from mine 2. The company wants to determine the number of hours it needs to operate each mine so that its contractual obligations can be met at the lowest cost.