Use Vogel’s method to find a bfs for Problems from previous Section.

A 1.0-kg standard cart A collides with a 0.10-kg cart B. The x component of the velocity of cart A is +0.60 m/s before the collision and +0.50 m/s after the collision. Cart B is initially traveling toward cart A at 0.40 m/s, and after the collision the x component of its velocity is +0.60 m/s. What are (a) the x component of the change in the momentum of A, (b) the x component of the change in the momentum of B, and (c) the sum of these two x components of the changes in momentum?

Round the monetary answer to the nearest dollar. Maria and Don had $20,800 in medical expenses. Their family medical insurance covered 60% of these expenses. The IRS allows medical and dental expense deductions for the amount that exceeds 7.5% of a taxpayer’s adjusted gross income. If their adjusted gross income is$101,598, how much can they claim as a medical deduction?

Change the infinitive to active if it is passive or into passive if it is active: narrare

General Ford produces cars at L.A. and Detroit and has a warehouse in Atlanta; the company supplies cars to customers in Houston and Tampa. The cost of shipping a car between points is given in Table 60 (“—” means that a shipment is not allowed). L.A. can produce as many as 1,100 cars, and Detroit can produce as many as 2,900 cars. Houston must receive 2, 400 cars, and Tampa must receive 1, 500 cars. a. Formulate a balanced transportation problem that can be used to minimize the shipping costs incurred in meeting demands at Houston and Tampa b. Modify the answer to part (a) if shipments between L.A. and Detroit are not allowed. c. Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of $5. TABLE 60:

$$\begin{matrix} \text{From} & \text{To (\$)}\\ \text{ } & \text{L.A.} & \text{Detroit} & \text{Atlanta} & \text{Houston} & \text{Tampa}\\ \text{L.A.} & \text{0} & \text{140} & \text{100} & \text{90} & \text{225}\\ \text{Detroit} & \text{145} & \text{0} & \text{111} & \text{110} & \text{119}\\ \text{Atlanta} & \text{105} & \text{115} & \text{0} & \text{113} & \text{78}\\ \text{Houston} & \text{89} & \text{109} & \text{121} & \text{0} & \text{—}\\ \text{Tampa} & \text{210} & \text{117} & \text{82} & \text{—} & \text{0}\\ \end{matrix}$$

An asset with an unadjusted basis of $\$50,000$ was depreciated over $n _ { \mathrm { tax } } = 10$ years for tax depreciation purposes and $n _ { \mathrm { book } } = 5$ years for book depreciation purposes. The annual depreciation was $1/n$ using the relevant life value. Use a spreadsheet to plot on one graph the annual book value for both methods of depreciation.

Use the northwest corner method to find a bfs for Problems from previous Section.

Use the transportation simplex to solve Problem. A company supplies goods to three customers, who each require 30 units. The company has two warehouses. Warehouse 1 has 40 units available, and warehouse 2 has 30 units available. The costs of shipping 1 unit from warehouse lo customer are shown in Table 7. There is a penalty for each unmet customer unit of demand: With customer 1, a penalty cost of $90 is incurred; with customer 2,$80; and with customer 3, $110. Formulate a balanced transportation problem to minimize the sum of shortage and shipping costs. Table 7:

$$\begin{matrix} \text{ } & \text{To}\\ \text{From} & \text{Customer 1} & \text{Customer 2} & \text{Customer 3}\\ \text{Warehouse 1} & \text{\$15} & \text{\$35} & \text{\$25}\\ \text{Warehouse 2} & \text{\$10} & \text{\$50} & \text{\$40}\\ \end{matrix}$$

The Ayatola Oil Company controls two oil fields. Field 1 can produce up to 40 million barrels of oil per day, and field 2 can produce up to 50 million barrels of oil per day. At field 1, it costs $3 to extract and refine a barrel of oil; at field 2, the cost is$2. Ayatola sells oil to two countries: England and Japan. The shipping cost per barrel is shown in Table 12. Each day, England is willing to buy up to 40 million barrels (at $6 per barrel), and Japan is willing to buy up to 30 million barrels (at$6.50 per barrel). Formulate a balanced transportation problem to maximize Ayatola’s profits. Table 12:

$$\begin{matrix} \text{ } & \text{To (\$)}\\ \text{From (\$)} & \text{England} & \text{Japan}\\ \text{Field 1} & \text{1} & \text{2}\\ \text{Field 2} & \text{2} & \text{1}\\ \end{matrix}$$

The U.S. government is auctioning off oil leases at two sites: 1 and 2. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 40% of the land being auctioned. Cliff has bid $1,000/acre for site 1 land and$2,000/acre for site 2 land. Blake has bid $900/acre for site 1 land and$2,200/acre for site 2 land. Alexis has bid $1,100/acre for site 1 land and$ 1,900/acre for site 2 land. Formulate a balanced transportation model to maximize the government’s revenue.

The following problems refer to the Powerco example. Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in Table 42. a. The company’s goal is to minimize the cost of meeting customers’ demands. Find two optimal bfs for this transportation problem. b. Suppose that customer 2’s demand increased by one unit. By how much would costs increase? TABLE 42:

$$\begin{matrix} \text{From} & \text{To} & \text{ } & \text{ } & \text{Supply}\\ \text{ } & \text{Customer 1} & \text{Customer 2} & \text{Customer 3} & \text{ }\\ \text{Plant 1} & \text{\$55} & \text{\$65} & \text{\$80} & \text{35}\\ \text{Plant 2} & \text{\$10} & \text{\$15} & \text{\$25} & \text{50}\\ \text{Demand} & \text{10} & \text{10} & \text{10} & \text{ }\\ \end{matrix}$$

A shoe company forecasts the following demands during the next six months: month 1—200; month 2—260; month 3—240; month 4— 340; month 5—190; month 6—150. It costs $7 to produce a pair of shoes with regular-time labor (RT) and$11 with overtime labor (OT). During each month, regular production is limited to 200 pairs of shoes, and overtime production is limited to 100 pairs. It costs $1 per month to hold a pair of shoes in inventory. Formulate a balanced transportation problem to minimize the total cost of meeting the next six months of demand on time.

Steelco manufactures three types of steel at different plants. The time required to manufacture 1 ton of steel (regardless of type) and the costs at each plant are shown in Table 8. Each week, 100 tons of each type of steel (1, 2, and 3) must be produced. Each plant is open 40 hours per week, a Formulate a balanced transportation problem to minimize the cost of meeting Steelco’s weekly requirements, b Suppose the time required to produce 1ton of steel depends on the type of steel as well as on the plant at which it is produced. Could a transportation problem still be formulated? TABLE 8:

$$\begin{matrix} \text{ } & \text{Cost (\$)} & \text{ } & \text{ } & \text{Time (minutes)}\\ \text{Plant} & \text{Steel 1} & \text{Steel 2} & \text{Steel 3} & \text{ }\\ \text{1} & \text{60} & \text{40} & \text{28} & \text{20}\\\text{2} & \text{50} & \text{30} & \text{30} & \text{16}\\ \text{3} & \text{43} & \text{20} & \text{20} & \text{15}\\ \end{matrix}$$

TABLE 9:

$$\begin{matrix} \text{ } & \text{Time (minutes)} & \text{ } & \text{ }\\ \text{Plant} & \text{Steel 1} & \text{Steel 2} & \text{Steel 3}\\ \text{1} & \text{15} & \text{12} & \text{15}\\ \text{2} & \text{15} & \text{15} & \text{20}\\ \text{3} & \text{10} & \text{10} & \text{15}\\\end{matrix}$$

General Ford has two plants, two warehouses, and three customers. The locations of these are as follows: Plants: Detroit and Atlanta Warehouses: Denver and New York Customers: Los Angeles, Chicago, and Philadelphia Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. Detroit can produce 150 cars per week, and Atlanta can produce 100 cars per week. Los Angeles requires 80 cars per week; Chicago, 70; and Philadelphia, 60. It costs $10,000 to produce a car at each plant, and the cost of shipping a car between two cities. Determine how to meet General Ford’s weekly demands at minimum cost.