A production manager must decide how many units of three cus…

A production manager must decide how many units of three custom furniture products to manufacture today: Chairs (C), Tables (T), and Desks (D). The goal is to maximize profit while satisfying minimum customer order requirements and not exceeding current inventory of materials. The products require different amounts of Wood, Metal, and Labor Hours, and generate different profit margins. Product Wood Required (ft²) Metal Required (lbs) Labor Required (hrs) Profit per Unit Minimum Orders Chair (C) 6 4 3 $40 12 Table (T) 10 6 5 $75 5 Desk (D) 12 8 7 $95 3 Inventory Available: Wood: 300 ft² Metal: 240 lbs Labor: 175 hours Note: Non-integer production quantities are allowed. Round your final answers to two decimal place. How many tables should be produced to achieve the optimal profit? units At the optimal solution, what is the total amount of metal used (in pounds)? lbs What is the maximum total profit the company can earn under the given constraints? $

After solving an optimization model for warehouse space allo…

After solving an optimization model for warehouse space allocation, a supply chain analyst notices that the solution heavily favors one region, raising concerns from regional managers. To better support decision-making, the analyst decides to explore slightly different scenarios and present alternative feasible solutions. Which of the following best describes the analyst’s approach?

MediSure, a growing healthcare services provider, operates a…

MediSure, a growing healthcare services provider, operates a 24/7 call center to support patients, healthcare providers, and insurance partners. With call volumes rising across all hours, the operations team must determine an optimal staffing plan that minimizes labor costs while maintaining required service levels. The call center uses five fixed 8-hour shifts to provide overlapping coverage throughout the day. Every agent is assigned to exactly one shift per day, and part-time scheduling is not permitted. Each 2-hour period throughout the day has a minimum number of agents that must be available to handle projected call volume. Time Period Minimum Agents Required 6:00 AM – 8:00 AM 35 8:00 AM – 10:00 AM 68 10:00 AM – 12:00 PM 52 12:00 PM – 2:00 PM 77 2:00 PM – 4:00 PM 60 4:00 PM – 6:00 PM 69 6:00 PM – 8:00 PM 74 8:00 PM – 10:00 PM 41 10:00 PM – Midnight 47 Midnight – 6:00 AM 18   Shift Shift Time Cost per Agent (Daily) Shift 1 6:00 AM – 2:00 PM $165 Shift 2 8:00 AM – 4:00 PM $150 Shift 3 12:00 PM – 8:00 PM $170 Shift 4 4:00 PM – 12:00 AM $185 Shift 5 10:00 PM – 6:00 AM $200 At the optimal solution, how many agents are scheduled to work during the 2:00 PM to 4:00 PM time period? agents At the optimal solution, how many agents should be assigned to Shift 4 (4:00 PM to 12:00 AM)? agents What is the minimum total labor cost required to meet all staffing requirements? $

A manufacturing firm operates three factories—Factory A, Fac…

A manufacturing firm operates three factories—Factory A, Factory B, and Factory C—that distribute goods to four retail stores. Each factory has a specific daily production capacity and may ship goods to any of the four stores. However, the total production capacity across all factories exceeds the total daily demand of the stores. Because the company does not have storage facilities, any unused capacity results in idle resources and should be minimized if possible. Factory A can produce up to 250 units per day, Factory B can produce 250 units, and Factory C can produce 200 units. The daily demand at the four stores is as follows: Store 1 requires 180 units, Store 2 requires 160 units, Store 3 requires 120 units, and Store 4 requires 140 units. The cost (in dollars) to ship one unit from each factory to each store is given in the table below: Shipping Cost per Unit ($) Store 1 Store 2 Store 3 Store 4 Factory A $4 $6 $9 $5 Factory B $7 $5 $4 $6 Factory C $6 $8 $3 $7 Determine the optimal shipping quantities from each factory to each store in order to minimize the total transportation cost, while ensuring that each store’s demand is fully met and no factory exceeds its daily production capacity. At the optimal solution, how many units should Factory B produce to meet the distribution plan? units At the optimal solution, how many units should Factory B ship to Store 2? units What is the minimum total shipping cost required to satisfy all store demands? $