Math Assignment
1. Solve the following system of equations
5x + 4y - z = 0
10y - 3z = 11
z = 3
2. A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.
If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?
3. A company makes two products (X and Y) using two machines (A and B). Each unit of X that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Y that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B.
At the start of the current week there are 30 units of X and 90 units of Y in stock. Available processing time on machine A is forecast to be 40 hours and on machine B is forecast to be 35 hours.
The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units. Company policy is to maximise the combined sum of the units of X and the units of Y in stock at the end of the week. (10 points)
• Formulate the problem of deciding how much of each product to make in the current week as a linear program.
• Solve this linear program graphically.
4. A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5000 for every acre of wheat and $3000 for every acre of barley that he plants. His use of pesticides is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide per acre and barley requires 1 gallon per acre.
What is the maximum profit he can make? How much wheat and barley should the farmer plant?
5. Find the compound amount and compound interest on the principle $20,000 borrowed at 6% compounded annually for 3 years.
6. Mr. Boutros wants to invest up to $20,000 in two stocks, Cal Computers and Texas Tools. The Cal Computers stock is expected to yield a 16% annual return, while the Texas Tools stock promises a 12% yield. Mr. Boutros would like to earn at least $2,880 this year.
According to Value Line Magazine's safety index (1 highest to 5 lowest), Cal Computers has a safety number of 3 and Texas Tools has a safety number of 2.
How much money should he invest in each to minimize the safety number? Note: A lower safety number means less risk.