A furniture company produces tables, chairs and benches, and sells these separately or in sets. For a table they need 12 units wood and 3 units metal. For a bench it is 6 units wood, 2 units metal and 5 units fabric. A chair is made from 2 units wood, 1 unit metal and 2 units fabric. Two types of sets are composed: set A consists of a table and four chairs, and set B contains a table, three chairs and a bench. a) Find the production matrix M that is used to calculate the necessary amounts of wood, metal and fabric to produce x tables, y chairs and z benches. b) Find the production matrix P that is used to calculate the necessary amounts of wood, metal and fabric to produce m sets of type A and n sets of type B. c) An order is for 40 sets of type A, 60 sets of type B and 10 (extra) benches. How many units of wood, metal and fabric are needed for this order?

Find the area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2. A = 6V2

Fire departments in your county have an average benchmark of 6 minutes on a fire call from the time the 911 operator takes the call to the time the first firefighter arrives on the scene. This 6-minute average includes a 1-minute call handling time from when 911 gets the call to when they notify the fire department. There is a 1-minute time from when the firefighters are notified to when they get out of the fire station. Then they have 4 minutes from when they leave the station to when they arrive on scene. Two fire departments in your county are being compared. From one fire department, a random sample of 10 calls has a mean of 6.51 minutes total with a standard deviation of 0.26 minutes. From the other fire department, a random sample of 11 calls shows a mean of 6.42 minutes with a standard deviation of 0.19. Construct a 90% confidence interval for the difference in the mean call time between the two fire departments. Fire departments in your county have an average benchmark of 6…

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