Hi im a new sophomore and im taking linear math 151 but im extremely weak in graphs and linear programming. I was doing my homework an came across a few problems that i could not solve. If someone could give me pointers as to how to do them or provide me with a solution i`ll be extremely thankful.
1. National Business Machines manufactures two models of fax machines: A and B. Model A costs $100 to make and model B costs $150. The profit for model A is $30 and the profit for model B is $40. If total number of fax machines demanded for each month does not exceed 2500 and the company has earmarked no more than 600,000/month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profits? what is the optimal profit?
2. A financier plans to invest up to 500,000 in two projects. Project A yields a return of 10% on the investment, whereas project B yields a return of 15% on the investment. Because the invest in project B is riskier than the investment in project A, she has decided that the investment in project B should exceed 40% of the total investment. how much the financier invest in each project in order to maximize the return on her investment? what is the maximum return?
3. A farmer plans to plant two crops, A and B. the cost of cultivating crop A is $40/acre, whereas that of crop is $60/acre. The farmer has a maximum of $7400 for land cultivation. Each acre of crop A requires 20 labor-hours and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor hours available. If she expects to make a profit of $150/acre on a crop A and $200/acre on crop B how many acres of crop should she planbt in order to maximize her profit? what is the optimal profit?