If the beginning finished goods -9 inventory 90 000 ID, ending finished goods inventory 65 000 ID, overhead expenses 18 000 ID ,cost of goods manufacturing 431 000 ID ,the * -: cost of goods sold is 654 000 ID. 546 000 ID. O 456 000 ID .00 O
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- Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 14) A paint supply company makes three styles of Paint Rollers, regular, deluxe andheavy. All of the types of brushes must pass through 3 machines. The different typesof brushes have the following contributions to profit per case and require thefollowing times (in hours) at each machine per case:Model Machine 1 Machine 2 Machine 3 Profit MarginRegular 3 2 3 $20Deluxe 2 4 4 40Heavy 4 4 5 70The company has 56 hours available for machine 1, 80 hours for machine 2 and 120 hoursfor machine 3. Assuming that the company is interested in maximizing the total profitcontribution, write the linear programming model for this problem.
- A software organisation employs 80,000 staff members. 16,000 employees are inthe sales team, 24,000 are in the customer support team and 14,000 are in thesoftware development and HR departments. What percentage of theorganisation’s employees are a part of the finance team, if the size of the financeteam makes up two-fifths of the remainder?Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $13,000. Assuming the college wishes to offer a total of six sections, accommodate 210 students, and bring in $253,000in revenues, how many sections of each course should it offer? Finite Math section(s)Applied Calculus section(s) Computer Methods section(s)A management consulting firm has four types of professionals on its staff: Managing consultants, senior associates, field staff and office staff. Average rates charged to consulting clients for work of each of these professionals categories are k3150/hour, k1680/hour, k1260/hour and k630/hour, respectively. Office records indicate the following number of hours billed last year in each category: 8,000, 14,000, 24,000 and 35,000, respectively. If the firm is trying to come up with an average billing rate for estimating client charges for next year, what would you suggest they do and what do you think is the appropriate rate?
- A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and plant Il needs at least 32 engines. The company can send at most 120 engines to these assembly plants. It costs $30 per engine to ship to plant I and $40 per engine to ship to plant Il. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant Il gives similar $10 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant I is() The number of engines to send to plant Il is() What is the minimum shipping cost, subject to the given constraints?$ ()4) A paint supply company makes three styles of Paint Rollers, regular, deluxe andheavy. All of the types of brushes must pass through 3 machines. The different typesof brushes have the following contributions to profit per case and require thefollowing times (in hours) at each machine per case: Model Machine 1 Machine 2 Machine 3 Profit MarginRegular 3 2 3 $20Deluxe 2 4 4 40Heavy 4 4 5 70 The company has 56 hours available for machine 1, 80 hours for machine 2 and 120 hoursfor machine 3. Assuming that the company is interested in maximizing the total profitcontribution, write the linear programming model for this problem.Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary — each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 2% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3. (a) Suppose that on March 3, 2022, one GPU is randomly selected from the day’s 70 units of production. That unit is found to be defective. What is the probability that that defective unit was produced by Machine 1? Machine 2? Machine 3? (b) Now suppose that on March 4, 2022, the firm operates only Machine 1. Of its 40 units…
- Consider a labor market for men and women with two types of workers in each group, high ability (H types), and low ability (L types). H types among men and women have a productivity of 70 and L types among men and women have a productivity of 30. Among women 2/3rds are H types, and 1/3rd are L types, and among men ½ are H types, and ½ L types. Suppose affirmative action for women reduces the cost of college for all women to 10. What happens to the average wage gaps between men and women? Recall that employers know the shares of H and L types, but cannot observe individual types. ● Women on average make around 12% more than men. ● Women on average will make 40% more than men. ● Men will make 40% more than women. ● Women on average make 2/3rds more than men.A private investment club has $200,000 earmarked for investment in stocks. To arrive at anacceptable overall level of risk, the stocks that management is considering have been classifiedinto three categories: high risk, medium risk, and low risk. Management estimates that high-riskstocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks,6%/year. The members have decided that the investment in low-risk stocks should be equal tothe sum of the investments in the stocks of the other two categories. Determine how much theclub should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment. (Assume that all the money available for investment isinvested.)Note: Develop the linear system of equations from the above theory and solve the system byGauss Jordon Method.HypertensionA national study found that treating people appropriately forhigh blood pressure reduced their overall mortality by 20%.Treating people adequately for hypertension has been difficult because it is estimated that 50% of hypertensives donot know they have high blood pressure, 50% of those whodo know are inadequately treated by their physicians, and50% who are appropriately treated fail to follow this treatment by taking the right number of pills.4.32 If the preceding 50% rates were each reduced to40% by a massive education program, then what effectwould this change have on the overall mortality rate amongtrue hypertensives; that is, would the mortality rate decreaseand, if so, what percentage of deaths among hypertensivescould be prevented by the education program?