3- Linear Programming Problem (20 points) The DISE Company has two plants; one in Warren, Michigan and the other in Springfield, Ohio, producing 1.6 L engines for the Lion's flagship passenger car, Luna. The orders from Lion's assembly plants have already been received for the next two months (June and July), where the numbers of engines requested are shown in Table 1. Due to an agreement, DISE needs to pay $105/month for each backordered 1.6 L engine. Monroe (MI) Dayton (OH) June July June July 1.6 L 2400 7600 3000 8000 Table 1. Monthly demand for 1.6 L engines in Lion's Monroe and Dayton plants. The available production days in June and July for DISE's Warren and Springfield plants are given in Table 2, whereas the daily production capacities in each plant is displayed in Table 3. Warren (MI) Springfield (OH) Warren Springfield June July June July 1.6 L 270 220 Days 21 19 22 20 Table 3. Daily production capacities able 2. Available production days in Warren and Springfield plants. Current inventory levels are 800 engines in Warren plant and 1000 in Springfield plant. In Warren plant, the cost of holding inventory is $12 per engine, whereas inventory holding cost in Springfield plant is $10 per engine. The unit production costs are shown in Table 4, whereas the shipping costs are given in Table 5. Warren Springfield Warren Springfield Monroe Dayton Monroe Dayton 1.6 L $220 $180 1.6 L $4 $18 $16 $5 Table 4. Unit production costs for 1.6 L engines. Table 5. Unit shipping cost for 1.6 L engines. The sales revenue the DISE receives when a plant sells the products to Lion's assembly plants are $450 for 1.6 L engines. Management now needs to determine the number of engines to be produced in each plant in each month, as well as the nu er of engines each plant shou sell to each assembly plant in June and July. Define decision variables and formulate to problem to maximize the total profit (total sales revenue minus sum of production costs, inventory costs, backordering costs, and shipping costs). 3- Linear Programming Problem (20 points) The DISE Company has two plants; one in Warren, Michigan and the other in Springfield, Ohio, producing 1.6 L engines for the Lion's flagship passenger car, Luna. The orders from Lion's assembly plants have already been received for the next two months (June and July), where the numbers of engines requested are shown in Table 1. Due to an agreement, DISE needs to pay $105/month for each backordered 1.6 L engine. Monroe (MI) Dayton (OH) June July June July 1.6 L 2400 7600 3000 8000 Table 1. Monthly demand for 1.6 L engines in Lion's Monroe and Dayton plants. The available production days in June and July for DISE's Warren and Springfield plants are given in Table 2, whereas the daily production capacities in each plant is displayed in Table 3. Warren (MI) Springfield (OH) Warren Springfield June July June July 1.6 L 270 220 Days 21 19 22 20 Table 3. Daily production capacities able 2. Available production days in Warren and Springfield plants. Current inventory levels are 800 engines in Warren plant and 1000 in Springfield plant. In Warren plant, the cost of holding inventory is $12 per engine, whereas inventory holding cost in Springfield plant is $10 per engine. The unit production costs are shown in Table 4, whereas the shipping costs are given in Table 5. Warren Springfield Warren Springfield Monroe Dayton Monroe Dayton 1.6 L $220 $180 1.6 L $4 $18 $16 $5 Table 4. Unit production costs for 1.6 L engines. Table 5. Unit shipping cost for 1.6 L engines. The sales revenue the DISE receives when a plant sells the products to Lion's assembly plants are $450 for 1.6 L engines. Management now needs to determine the number of engines to be produced in each plant in each month, as well as the nu er of engines each plant shou sell to each assembly plant in June and July. Define decision variables and formulate to problem to maximize the total profit (total sales revenue minus sum of production costs, inventory costs, backordering costs, and shipping costs)