Derry Retail is considering the quantity of smartwatches (150, 200, or 250 units) to order and,...

Transcribed Image Text:

Derry Retail is considering the quantity of smartwatches (150, 200, or 250 units) to order and, hopefully, sell during the next holiday sale. They believe there will be low demand (100 units) for the smartwatch with 30% chance, moderate demand (150 units) with 40% chance, and high demand with (200 units) with 30% chance. Derry buys each smartwatch at $240 and sells them for $400 each. Smartwatches not sold over the holidays are guaranteed to be sold off during post-holiday sale at $190 each. They decided to create a payoff model for generating gross profit as follows: Payoff = (price x minimum(order, demand)) - (cost x order) + post-holiday revenue (if any) Post-holiday revenue = maximum(post-holiday pricex (order-demand), 0) For example, if they order 250 units and demand is 150 units, their gross profit will be ($400 x 150) - ($240 x 250) + $190 x (250-150) = $19,000 Note: Post-holiday revenue can be only realized if supply is greater than demand. a) Use the given information to complete the following payoff table. PAYOFF TABLE Order 150 units $ Order 200 units Order 250 units Demand = 100 units Demand = 150 units $19,000 b) What is the expected value of the optimal decision? Demand = 200 units Derry Retail is considering the quantity of smartwatches (150, 200, or 250 units) to order and, hopefully, sell during the next holiday sale. They believe there will be low demand (100 units) for the smartwatch with 30% chance, moderate demand (150 units) with 40% chance, and high demand with (200 units) with 30% chance. Derry buys each smartwatch at $240 and sells them for $400 each. Smartwatches not sold over the holidays are guaranteed to be sold off during post-holiday sale at $190 each. They decided to create a payoff model for generating gross profit as follows: Payoff = (price x minimum(order, demand)) - (cost x order) + post-holiday revenue (if any) Post-holiday revenue = maximum(post-holiday pricex (order-demand), 0) For example, if they order 250 units and demand is 150 units, their gross profit will be ($400 x 150) - ($240 x 250) + $190 x (250-150) = $19,000 Note: Post-holiday revenue can be only realized if supply is greater than demand. a) Use the given information to complete the following payoff table. PAYOFF TABLE Order 150 units $ Order 200 units Order 250 units Demand = 100 units Demand = 150 units $19,000 b) What is the expected value of the optimal decision? Demand = 200 units