1. A small school held a fund raiser. A total of 23 adults and children attended. Each adult paid $10, and each child paid $2 to attend. If a total of $86 was raised, use a system of equations to determine how many adults and how many children attended. Solve the system using Gaussian Elimination.
2. Two zinc alloys contain 20% and 50% zinc. How many ounces of each alloy should be combined to form 30 ounces of a 45% zinc alloy. What would the objective function constraints be? Solve using linear programming
3. Find the value of c in the quadratic equation, y = ax + bx + c, if its graph passes through the points (1,0), (-1,-6), and (2,9).
4. A company produces both large and small cabinets. A small cabinet requires 1 hour of labor and a large cabinet requires 4 hours of labor. The company has at most 80 hours of labor available each day. No more than 60 small cabinets and no more than 15 large cabinets can be produced in a day due to space limitations. If the company's profit is $120 per small cabinet and $250 per large cabinet, how many of each should be produced to maximize profit? What is the maximum profit? What would the objective function constraints be? Solve using linear programming.
5. The sum of three integers is 15. The middle integer is 1 more than twice the smallest. The larger integer is 4 times the smallest. Use a system of equations to find the three integers.
6. A builder wants to build an apartment building of no more than 23,400 square feet and to divide it into one and two bedroom units. One bedroom units require 500 square feet and rent for $300 per month. Two bedroom units require 650 square feet and rent $350 per month. The market suggests that there be at least twice as many two bedroom units as on bedroom units. His financial backer wants the total number of apartments to be at least 21. Assuming the building will be fully occupied, and he wishes to maximize his rental income, what would the objective function constraints be? Find the max rental income. Solve using linear programming.