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Systems of Equations and Linear Programming : Six Word Problems

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See the attached file.
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.

(Problem set is also found in attachment).

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Solution Summary

Six word problems dealing with systems of equations and linear programming are solved. The solution is detailed and well presented.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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