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Why аre nоrms criticаl fоr persоnаlity and psychopathology assessment?
A regiоnаl big-bоx retаiler is heаding intо a high-demand promotional week and needs to move enough inventory from its central distribution center to multiple stores across the state. Based on store orders and historical sales patterns, the logistics team estimates that the company must deliver at least 600 pallets of mixed merchandise (household essentials, packaged food, and seasonal items) during the week to avoid stockouts and lost sales. The retailer has two transportation options through its contracted carriers. The first option is truck shipments, which are highly flexible and can be dispatched on short notice to match store needs. However, trucks are relatively expensive on a per-pallet basis. Each truck shipment can carry 30 pallets and costs $1,000. The second option is rail shipments, which are more cost-efficient for bulk movement but require advance scheduling and have less routing flexibility. Each rail shipment can carry 60 pallets and costs $3,600. In addition to meeting demand, the distribution center must operate within its handling capacity. Because of limited dock doors, forklift operator availability, and daily appointment slots for loading, the facility can process no more than 14 total outbound shipments (truck plus rail) during the week. Management wants to minimize transportation spending while still ensuring enough product reaches stores. According to the optimal solution, how many truck shipments should the retailer schedule? [x] shipments According to the optimal solution, how many rail shipments should the retailer schedule? [y] shipments What is the minimum total shipping cost that satisfies both requirements? $[cost]
BrightWаve Fitness Studiо is а fаst-grоwing bоutique gym in a midsize city that is preparing to launch a new “8-Week Transformation” program. The program is designed to attract busy professionals who want structured workouts, nutrition guidance, and progress tracking. Management expects strong interest, but competition from other gyms and wellness programs is intense. To ensure the new program fills up quickly, BrightWave plans a concentrated advertising push over the next several weeks. The studio’s marketing team has identified two advertising options that fit BrightWave’s audience. The first option is Instagram Story Ads (Option A), which can be targeted by age, location, and interests (fitness, wellness, weight loss). These ads tend to generate a steady flow of impressions among younger and middle-aged users who frequently scroll through Instagram. The second option is Local Podcast Sponsorship Ads (Option B), where BrightWave buys short ad reads on popular podcasts listened to by local commuters and professionals. Podcast sponsorships typically deliver higher impressions per placement because listeners often complete full episodes, but they require more coordination and lead time. The marketing team is choosing between two advertising options that reach BrightWave’s target audience. Option A is Instagram Story Ads, which can be precisely targeted by location and interests and typically perform well with younger and middle-aged fitness-minded consumers. Option B is Local Podcast Sponsorship Ads, where BrightWave purchases short host-read promotions on podcasts popular with local commuters and professionals; these placements often generate strong reach because listeners frequently complete full episodes. Based on prior results and vendor estimates, each Instagram ad buy generates about 10,000 impressions, and each podcast sponsorship generates about 12,000 impressions. BrightWave faces two weekly constraints. First, the campaign has a weekly advertising budget cap of $9,000, so the combined spending on Instagram and podcast ads cannot exceed $9,000 in any week. Second, the in-house creative team can devote at most 80 hours per week to producing and coordinating these ads. Each Instagram ad buy costs $200 and requires 3 creative hours, while each podcast sponsorship costs $300 and requires 2 creative hours. BrightWave’s goal is to decide how many units of each advertising option to purchase per week to maximize total weekly exposure (impressions) while staying within both the $9,000 budget and the 80-hour creative limit. How many units of Instagram Story Ads (A) should be purchased at the optimal solution? [A_units] units What is the maximum total exposure BrightWave can achieve at the optimal solution? [max_exposure] impressions At the optimal solution, how many creative team hours are used? [creative_hours] hours