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Math Word Problems (Intermediate Algebra)
I need some help on solving these two problems. Can anyone offer any help?
Question 1:
George, from "George World Businesses" (a dubious contracting firm), has contacted you to help him determine the profitability of his new painting business. He can buy white paint in 50 Gallon barrels for $250 each. When brushed or sprayed, the wet paint lays on the wall with a thickness of 0.010 inches. A professional painter will paint at a rate of 150 square feet per hour (2 coats), and an apprentice will take three times as long. According to George's business practices, he will hire 4 apprentices for every professional painter. The professional will command an hourly rate of $15, while the apprentices have to accept the State's minimum wage of $ 2.75 per hour. George has to pay insurance premiums and taxes, equivalent to 30% of his payroll.
The State has requested bids to paint (inside and out) two empty state office buildings. The buildings are two story 100 x 50 square feet rectangles, in which each floor, including the basement, is 10 feet high with a 1 foot thickness between the ceiling and the floor of the next story. Each building has 20 4x4 square feet windows and 2 4x9 square feet doors. The job has to be done in 5 business days. In addition to his useful personnel, George has to hire his wife's college room mate, who has no experience working on anything but demands a professional's salary.
Of course, George wants to make some money, no less than a 50% profit off this government contract. The question for you is, what composition of labor force should he hire and how much money he should request on his bid.
Can you use graphics or charts to show your results?
Question 2:
Sven is an investor with money burning a hole in his pocket. He is thinking of creating a manufacturing business that makes and directly sells gadgets. He figured that the fixed costs of his factory (rent, equipment, insurance, etc.) for one year is going to cost him $150,000. The material to make the gadgets costs about $ 0.16 per gadget and the energy required to manufacture them runs about $ 0.35 per gadget. The factory, as he has envisioned it, has a maximum capacity of 4,000 gadgets per month. He has hired you to analyze his options and make projections and recommendations regarding price, production schedules, and quality. Essentially, Sven wants to know his limitations on price and quality, not to lose any money on that first year, and he expects you to use clear reasoning, and graphics to make your point.
In this context, quality means how many gadgets can he afford to throw in the trash due to quality issues.
Thanks
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