MATH 5845- FALL 2018 Worksheet 4 Name: Show all work clearly and in order. Justify your answers when possible. 1(3 points) Leary Chemical manufactures three chemicals: A. B and C. These chemicals are produced via two production processes: I and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B and I of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 unit of B. To meet customer demands, at least 10 units of A, 5 of B and 3 of C must be produced daily. Graphically determine a daily production plan that minimizes the cost of meeting Leary Chemical's daily demands. 2. (3 points) For each of the following, determine the direction in which the objetive function increases: 3.1-32 3. (4 points) Farmer Jane owns 45 acres of land. She is going to plant cach with wheat or corn. Eadh acre panted with wheat yields $200 profit; each with corm yields $300 profit. The labor and fertilizer used for each acre are given in Table 1. One hundred workers and 120 tons of fertilizer are available. Use linear programming to determine how Jane can maximizes profits from her land. Wheat Corn Labor 3 workers 2 workers Fertilizer 2 tons 4tons MATH 5845- FALL 2018 Worksheet 4 Name: Show all work clearly and in order. Justify your answers when possible. 1(3 points) Leary Chemical manufactures three chemicals: A. B and C. These chemicals are produced via two production processes: I and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B and I of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 unit of B. To meet customer demands, at least 10 units of A, 5 of B and 3 of C must be produced daily. Graphically determine a daily production plan that minimizes the cost of meeting Leary Chemical's daily demands. 2. (3 points) For each of the following, determine the direction in which the objetive function increases: 3.1-32 3. (4 points) Farmer Jane owns 45 acres of land. She is going to plant cach with wheat or corn. Eadh acre panted with wheat yields $200 profit; each with corm yields $300 profit. The labor and fertilizer used for each acre are given in Table 1. One hundred workers and 120 tons of fertilizer are available. Use linear programming to determine how Jane can maximizes profits from her land. Wheat Corn Labor 3 workers 2 workers Fertilizer 2 tons 4tons