Suppose that April's Pet Supply has three stores in cities 1, 2, and 3. Ben's Pet Mart has three stores in in cities 1, 2, and 3. Each shop sells the same type of dog crates in sizes 1 (small), 2 (medium), 3 (large), and 4 (extra large). April's and Ben's inventory in each city is stored in the tables below. Size 1 Size 2 Size 3 Size 4 City 1 3 April's Pet Supply City 2 4 1 0 5 2 4 0 City 3 1 9 2 1 Size 1 Size 2 Size 3 Size 4 City 1 2 0 4 0 Ben's Pet Mart City 2 3 2 1 0 City 3 4 4 3 2 1. Create matrices A and B representing the values in the tables above such that the rows represent the different options and the columns represent the different outcomes of each option. 2. Suppose that April and Ben merge their inventories. Find a matrix that represents their combined inventory in each of the three cities. 3. Calculate B-A. What does B - A represent?

A clothing retailer must decide how many boxes of fashion pants to order for the upcoming season. The pants in question come in boxes of 100, 200, and 300, and the retailer has decided to order exactly one of the three types of boxes. Naturally, there is a quantity discount: each pair of pants in the small box costs $5, in the regular box the price is $4 for a pair, & in the big box it is $3 per pair. Individual orders for pairs are, however, not possible. Demand has been estimated at either 10, 30, 70 or 80 pairs, and the probabilities for these demands are thought to be 0.2, 0.4, 0.3, and 0.1. Pants sell for $10 a pair, and customer demand must be satisfied. In case the store does not have sufficient supplies, they must purchase them from one of their competitors at $13 per pair. Pants left unsold have a salvage value of $1 each. Which of the boxes should be ordered and what is the expected profit? Show all relevant computations.

Rs

The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture—wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows:Resource Requirements                            Wood (board ft.)       Upholstery (yd.)            Labor (hr.)Sofa                            7                            12                                  6Table                        5                               —                                 9Chair                         4                             7                                    5                Total available resources 2,250              1,000                              240The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture.…