Chapter 7 Assignment Problems 1. 7.26 from end of the chapter. Use iso-profit or corner point method. 2. Zara stores in the United States stocks a particular type of designer denim jeans in the United States. It stores 500 pairs of jeans each month from its two suppliers. The Hong Kong supplier charges Zara $11 per pair of jeans, and the Colombian supplier charges $16 per pair (and then Zara marks them up almost 1,000%). Although the jeans from Hong Kong are less expensive, they also have more defects than those from Colombia. Based on past data, Zara estimates that 7% of the Hong Kong jeans will be defective compared to only 2% from Colombia and Zara does not want to import any more than 5% defective items. However, Zara does not want to rely on a single supplier, so it wants to order at least 20% from each supplier every month. a. Formulate a linear programming model for this problem. b. Solve the linear programming model graphically. Use either iso-line or corner point method. How many of each should Zara buy? c. How much will Zara pay for them? d. If the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to %5, what would be the effect on the solution. Solve c in a separate sheet. First copy the sheet you solved a, b and c. Then change the necessary line and re-solve. 3. Schwinn holds 3 type of bicycles: race bikes, cross-country bikes, and trail bikes. He sells race bikes for $1,900, cross-country bikes for $2,200 and trail bikes for $1300. A race bike costs $1,300, a cross-country bike costs $1,800 and a trail bike costs $1000. He has $12,000 available this month to purchase bikes. Each bike requires assembly: a race bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a trail bike requires 16 hours. He and his employees have 120 hours available to put the bikes together. He has enough space in his store to order 20 bikes this month. Schwinn wants to stock at least twice as many trail bikes as the other two combined. a. Formulate a linear programming model for this problem. b. Solve the linear programming model using excel Solver. What is the maximum profit? c. How many bicycles should he purchase from each? d. What should Schwinn do to increase profit based on the optimal solution? e. If Schwinn hired an additional worker for 40 hours at least $10 per hour, how much additional profit would he make, if any? Use LP Template as demonstrated in videos. I will delete your decision variables in your Excel submission and re-solve your problem. There is no credit for the problem if your Excel submission doesnt solve.

problem #1:

use the following template to solve problem #3:

The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than permitting the olives to grow on their own and results in a smaller size olive. It also permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the normal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the maximum possible profit. (b) the best combination of barrels of pruned and regular olives. (c) the number of acres that the olive grower should devote to each growing process