1. A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours, while each unit of products B and C requires 5 hours. The company realizes a profit of $500 for each unit of product A, $600 for each unit of product B, and $1,000 for each unit of product C. Formulate (and solve) a linear program to determine how many units of each of the three products the company should make to maximize profits.
2. A bank loaned $15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was $1800, how much was loaned at 10%?
Let's call Qa, Qb and Qc respectively to the quantities produced of goods A, B and C. The objective of the firm is to maximize profits, so the objective function should be:
max 500*Qa + 600*Qb + 1000*Qb
That is, choose Qa, Qb and Qc so that profits (the above equation) is maximized. There are two restrictions, however. The company can't use more than 500 pounds of the raw material. The amount of raw material used for the whole production of good A is ...
This solution solves two linear programming questions, addressing maximizing profit and income loans.