1a) A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottawa. One month the shop ordered a total of 90units of yarn from these suppliers. The delivery costs were$83, $48, and $64

per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $5289 The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier?

There were_ units ordered from Toronto,_ units from Montreal, and_units from Ottawa.

 

1b) A furniture factory has 2750 machine hours available each week in the cutting department,1420 hours in the assembly department, and 2970 in the finishing department. Manufacturing a chair requires

0.7 hours of cutting, 0.1 hours of assembly, and 0.8 hours of finishing. A cabinet requires 0.2 hours of cutting, 0.4 hours of assembly, and 0.6 hours of finishing. A buffet requires 0.6 hours of cutting,0.3

hours of assembly, and 0.1 hours of finishing. How many chairs, cabinets, and buffets should be produced in order to use all the available production capacity?

 

1c) The U-Drive Rent-A-Truck company plans to spend $16 million on 320 new vehicles. Each commercial van will cost $25,000 each small truck $80,000 and each large truck $70,000 Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?

1d) Use the Gauss-Jordan method to solve the following system of equations.

3x+2y=1

 -6x-4y=-2

 

1e) Use the Gauss-Jordan method to solve the following system of equations.

        9x-4y=63

       18x-8y=7