Steinwelt Piano manufactures uprights and consoles in two plants, plant I and plant II. The output of plant I is at most 210 pianos/month, whereas the output of plant II is at most 175 pianos/month. These pianos are shipped to three warehouses that serve as distribution centers for the company. To fill current and projected orders, warehouse A requires a minimum of 140 pianos/month, warehouse B requires at least 105 pianos/month, and warehouse C requires at least 140 pianos/month. The shipping cost of each piano from plant I to warehouse A, warehouse B, and warehouse C is $60, $60, and $80, respectively, and the shipping cost of each piano from plant II to warehouse A, warehouse B, and warehouse C is $90, $70, and $50, respectively. Use the method of this section to determine the shipping schedule that will enable Steinwelt to meet the warehouses' requirements while keeping the shipping costs to a minimum.
A) 0, 35 and 140 pianos form plant I to warehouse A, warehouse B and warehouse C respectively.
140, 70 and 0 pianos form plant II to warehouse A, warehouse B and warehouse C respectively.
B) 0, 40 and 160 pianos form plant I to warehouse A, warehouse B and warehouse C respectively.
160, 80 and 0 pianos form plant II to warehouse A, warehouse B and warehouse C respectively.
C) 160, 80 and 0 pianos form plant I to warehouse A, warehouse B and warehouse C respectively.
0, 40 and 160 pianos form plant II to warehouse A, warehouse B and warehouse C respectively.
D) 100, 50 and 0 pianos form plant I to warehouse A, warehouse B and warehouse C respectively.
0, 25 and 100 pianos form plant II to warehouse A, warehouse B and warehouse C respectively.
E) 140, 70 and 0 pianos form plant I to warehouse A, warehouse B and warehouse C respectively.
0, 35 and 140 pianos form plant II to warehouse A, warehouse B and warehouse C respectively.

Question

Quizplus · Accepted Answer

The correct shipping schedule must meet the minimum requirements of each warehouse while not exceeding the production capacities of both plants. Plant I can produce up to 210 pianos, and Plant II up to 175 pianos. Warehouse A requires 140 pianos, B requires 105, and C requires 140. The shipping costs also need to be minimized. Option E correctly allocates the production from Plant I and Plant II to meet the exact demands of warehouses A, B, and C without exceeding the production capacities of the plants. It also considers the cost-effectiveness of shipping pianos from each plant to the warehouses, with Plant I shipping to A and B where its costs are lower or equal, and Plant II shipping to C where its cost is lowest.

Steinwelt Piano Manufactures Uprights and Consoles in Two Plants, Plant