2. Transportation (8 POINTS) (Please Use Excel)

A shipping company has received an order to deliver the raw materials to the auto manufacturer from Question 1. Here is some information they have received about the raw materials:

Each unit of steel weighs 30 lbs, has a volume of 8 cubic feet, and has a value of $850.

Each unit of glass weighs 39 lbs, has a volume of 6 cubic feet, and has a value of $640.

Each unit of plastic weighs 16 lbs, has a volume of 14 cubic feet, and has a value of $575.

Each unit of paint weighs 65 lbs, has a volume of 3 cubic feet, and has a value of $350.

The shipping company has also received instruction from the auto manufacturer, to always deliver the same number of units of steel and plastic with each shipment. If the shipping companys largest cube van can carry up to 2,000 lbs, has volume of 580 cubic feet, and is insured for $41,830 of contents, how many units of each product can be delivered? Assume the company will want to ship the maximum amount possible, by fully utilizing all available capacities.

1. Automotive Business (17 POINTS) Suppose that an automobile manufacturer has accepted orders for 55 compact SUVs, 20 luxury SUVs, and 35 sedans. These orders can be represented by the row vector Q: Q = [55 20 35] The "raw materials" that go into each type of vehicle are steel, glass, plastic, paint, and labour. The entries in matrix R below give the number of units of each raw material (in the order stated) which are needed for each type of vehicle (in the order stated above). 17 4 7 5 5 R = 9 5 8 6 7 16 3 6 4 3 Suppose that steel costs $850 per unit, glass costs $640 per unit, plastic costs $575 per unit, paint costs $350 per unit, and labour costs $1200 per unit. This data can be written as the column cost vector C: 850 640 575 350 1200 The price the manufacturer negotiated for each compact SUV is $32,000, for each luxury SUV is $47,000, and for each sedan is $35,000. This information can be written as the column price vector P: [32000 P = 47000 L35000) a) Find the total amount of each raw material the manufacturer will need to fill all the orders. (4 POINTS) b) Find the total cost of each type of vehicle (i.e. the cost of raw materials, including labour, to produce just one of each type of vehicle). (4 POINTS) c) Find the total cost of raw materials for these order (i.e. the total cost of all vehicles of all types). (4 POINTS) d) Find the profit made by the manufacturer on these orders. (5 POINTS) 1. Automotive Business (17 POINTS) Suppose that an automobile manufacturer has accepted orders for 55 compact SUVs, 20 luxury SUVs, and 35 sedans. These orders can be represented by the row vector Q: Q = [55 20 35] The "raw materials" that go into each type of vehicle are steel, glass, plastic, paint, and labour. The entries in matrix R below give the number of units of each raw material (in the order stated) which are needed for each type of vehicle (in the order stated above). 17 4 7 5 5 R = 9 5 8 6 7 16 3 6 4 3 Suppose that steel costs $850 per unit, glass costs $640 per unit, plastic costs $575 per unit, paint costs $350 per unit, and labour costs $1200 per unit. This data can be written as the column cost vector C: 850 640 575 350 1200 The price the manufacturer negotiated for each compact SUV is $32,000, for each luxury SUV is $47,000, and for each sedan is $35,000. This information can be written as the column price vector P: [32000 P = 47000 L35000) a) Find the total amount of each raw material the manufacturer will need to fill all the orders. (4 POINTS) b) Find the total cost of each type of vehicle (i.e. the cost of raw materials, including labour, to produce just one of each type of vehicle). (4 POINTS) c) Find the total cost of raw materials for these order (i.e. the total cost of all vehicles of all types). (4 POINTS) d) Find the profit made by the manufacturer on these orders. (5 POINTS)