A computer company has manufacturing plants in Raleigh and Palo Alto. The Raleigh plant manufactures 330 keyboards per week, whereas the Palo Alto plant produces 670. The company has stores in Chicago and Denver. The Chicago store orders 590 keyboards per week and the Denver store orders 410. The shipping costs per keyboard from each factory to each store are as follows: Raleigh to Chicago: $7 Raleigh to Denver $10 Palo Alto to Chicago: $12 Palo Alto to Denver: $9

The Collin Freight Company has an order for three products to be delivered to a      destination. Product I requires 10 cubic feet, weighs 10 pounds, and has a value      of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20.      Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the      carrier can carry 6,000 cubic feet, 11,000 pounds, and is insured for $36,900, how      many of each product can be carried?     a. Identify the variables of the problem using x, y and z.     b. Fill out the following table from the information given:                                                                                 total  Volume (cu. ft.)  Weight (lb.)  Value ($)     c. Write the augmented matrix for the system of equations. d. Solve the system of equations using Gauss-Jordan Elimination.                   e. In at least one complete sentence, answer the question: How many of each productcan be carried?

A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Hauling Cost per Ton at Site Pit 1 3 Price per Ton North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site. a. Formulate this problem as an assignment problem by constructing the appropriate cost table,…

A campus student group is raising funds for charity by selling cups of boba tea. The expenses incurred by this student group are the cost of materials, estimated at $2 per cup (tea, boba, milk, sugar, cups, the big honking straws, napkins, etc.) and the $150 cost of renting the brewing and cooking space. The group will charge students $4 for each cup.a. Write down the associated cost, revenue, and profit functions. b. How many cups of boba must they sell to break even?c. What profit (or loss) results from the sale of 50 cups?