A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce at least 410 tons of regular-grade and 530 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per hour. The second mine produces 20 tons of regular-grade and 10 tons of low-grade ore per hour. The operating cost of the first mine is $9000 per hour, and the operating cost of the second mine is $30,500 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no more than 29 hours a week. How many hours per week should each mine be operated to minimize the cost? First Mine: __ hours Second Mine:__ hours

There are 10 forging presses in the forge shop of a small company. The shop produces batches of forgings requiring a setup time of 2.0 hours for each production batch. Average standard time for each part in a batch is 30 seconds, and there are an average of 500 parts in a batch. The plant workforce consists of two workers per press, one foremen, plus two clerical support staff. (a) Determine how many forged parts can be produced in 1 month, if there are 8 hours worked per day and an average of 21 days per month at one shift per day. (b) What is the labor productivity ratio of the forge shop, expressed as parts per worker-hour?

To receive a grade of A, the average of four 100-point exams must be 90 or better. If a student received scores of 87, 84, and 95 on the first three exams, what minimum score does he need on the fourth exam to earn an A?

A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 4 to 3. The amount of nitrogen must be at least 42 kg. The percent of nitrogen in the three chemicals is 7%, 3%, and 4%, respectively. If the three chemicals cost $1.08. $0.86, and $0.65 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 750 kg of the plant food? The minimum cost plant food is made with kg of chemical 1 kg of chemical II, andkg of chemical III (Type integers or decimals. Round to one decimal place as needed.)

The quarrying cost of marble and granite blocks plus delivery cost to the processing plant is ₱9,600 per cubic meter. Processing cost of marble into tiles is ₱800 per square meter and that of granite into tiles also is ₱2,400 per square meter.A marble has a net yield of 40 square meters of tiles per cubic meter of block and sell at ₱1600 per square meter, and granite gives a net yield of 50 square meters of tiles per cubic meter of block and sells at ₱4,000 per square meter. Considering all other cost to be the same, determine the more profitable material and by how much. Solve and show the solution.

A goal is to get at least 10% of daily calories from polyunsaturated fats as are found in various nuts, oils, and fish. One serving of walnuts (about 15 pieces) has about 20 g of polyunsaturated fat. Each fat gram has 9 calories. About what percent of daily calories does one serving of walnuts provide, assuming a 2,000-calorie diet?

Glueco produces three types of glue on two differentproduction lines. Each line can be utilized by up to sevenworkers at a time. Workers are paid $500 per week onproduction line 1, and $900 per week on production line 2.A week of production costs $1,000 to set up production line1 and $2,000 to set up production line 2. During a week ona production line, each worker produces the number of unitsof glue shown in Table 12. Each week, at least 120 units ofglue 1, at least 150 units of glue 2, and at least 200 units ofglue 3 must be produced. Formulate an IP to minimize thetotal cost of meeting weekly demands.

Students are going through a three-step process to obtain their ID cards. Each student will spend 2 minutes at the registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he/she will visit one of four ID processing stations to have his/her picture taken and ID card printed. Visits to the cashier and ID processing station take 10 and 20 minutes respectively. If the demand rate is 0.5 student per minute, the cycle time of the process is type your answer. minute per student (rounded to Nearest 10th); and bottleneck in the process is TD. Peo choose your answer. use Excel

A mining company has two mines. One day's operation at mine #1 produces ore that contains 10 metric tons of copper and 590 kilograms of silver, while one day's operation at mine 10 and V₂ = #2 produces ore that contains 20 metric tons of copper and 550 kilograms of silver. Let v₁ 20 550 Then v₁ and v₂ represent the "output per day" of mine #1 and 590 mine #2, respectively. Complete parts (a) through (c) below. a. What physical interpretation can be given to the vector 2v₁? O A. It is the output of copper at mine #1 after 2 days of operation. B. It is the output at mine #1 after 2 days of operation. O C. It is the output at mine #2 after 2 days of operation. OD. It is the output of silver at mine #1 after 2 days of operation. C... b. Suppose the company operates mine #1 for x₁ days and mine #2 for x₂ days. Write a vector equation in terms of v₁ and v₂ whose solution gives the number of days each mine should operate in order to produce 72 tons of copper and 2610 kilograms of silver. Do…

An online retailer requires three different size containers to package its products for shipment. The costs of these containers A, B, and C, and their capacities are shown as follows:             Container         A          B          C             Cost ($ each)     4          6          7             Capacity (cu in) 200       400      600 If the retailer orders 2500 containers with a total capacity of 1,100,000 cu in at a cost of $15,000, how many of each are in the order?