1. A candy manufacturer has 500 lb. of chocolate, 100 lb. of nuts, and 50 lb. of fruit in inventory. She produces three types of candy. A box of type A requires 3 lb. of chocolate, 1 lb. of nuts, and 1 lb. of fruit and sells for $50. A box of type B requires 4 lb. of chocolate and 1 lb. of nuts and sells for $30. A box of type C requires 5 lb. of chocolate and sells for $20. Assuming she can sell all the candy she makes, how many boxes of each type of candy should she make in order to maximize her income? What is the maximum income?
Find the solution to this problem using the simplex algorithm and confirm your solution using the solver tool in Excel.
2. A small business mass-produces three types of decorative wooden sculptures. Sculpture A requires 4 hours to cut the wood, 2 hours to assemble, and 1 hour to apply the finish and sells for $500. Sculpture B requires 2 hours to cut the wood, 2 hours to assemble, and 3 hours to apply the finish and sells for $300. Sculpture C requires 4 hours to cut the wood, 3 hours to assemble, and 2 hours to apply the finish and sells for $400. There are two employees who cut the wood, one who assembles the sculptures, and one who applies the finish. Each worker can work, at most, 40 hours a week except the assembler who can work 50 hours a week. How many of each type of sculpture should be made in order to maximize the revenue? What is the maximum revenue?
Find the solution to this problem using the simplex algorithm and confirm your solution using the solver tool in Excel.
3. On average, an adult male under the age of 50 requires at least 32 grams of fiber per day and at least 60 grams of protein. A survivalist has a supply of two types of dietary supplements. The type-A supplement is 20% fiber and 50% protein (by weight). The type-B supplement is 32% fiber and 30% protein (by weight). How many grams of each type of supplement are needed to satisfy the minimum daily requirements for fiber and protein if the total weight is to be as small as possible?
Find the solution to this problem using the simplex algorithm and confirm your solution graphically and by using the solver tool in Excel.