A store wants to determine how many Christmas trees it should order for the holiday season. The store purchase these trees at a price of $240 per tree and sells them for $300 per tree. The demand for them during the season normally distributed with a mean of 90 trees and a standard deviation of 10 trees. Any unsold trees are always eventually sold but at discount of 30%. Determine the optimal stocking level?
A store wants to determine how many Christmas trees it should order for the holiday season. The store purchase these trees at a price of $240 per tree and sells them for $300 per tree. The demand for them during the season normally distributed with a mean of 90 trees and a standard deviation of 10 trees. Any unsold trees are always eventually sold but at discount of 30%. Determine the optimal stocking level?
Related questions
Polaski Company manufactures and sells a single product called aRet. Operating at capacity, the company can produce and sell 34,000Rets per year. Costs associated with this level of production andsales are given below:
| Unit | Total | ||||
| Direct materials | $ | 20 | $ | 680,000 | |
| Direct labor | 8 | 272,000 | |||
| Variable manufacturingoverhead | 3 | 102,000 | |||
| Fixed manufacturingoverhead | 7 | 238,000 | |||
| Variable selling expense | 2 | 68,000 | |||
| Fixed selling expense | 6 | 204,000 | |||
| Total cost | $ | 46 | $ | 1,564,000 | |
The Rets normally sell for $51 each. Fixed manufacturingoverhead is constant at $238,000 per year within the range of26,000 through 34,000 Rets per year.
Required:
1. Assume that due to a recession, Polaski Company expects tosell only 26,000 Rets through regular channels next year. A largeretail chain has offered to purchase 8,000 Rets if Polaski iswilling to accept a 16% discount off the regular price. There wouldbe no sales commissions on this order; thus, variable sellingexpenses would be slashed by 75%. However, Polaski Company wouldhave to purchase a special machine to engrave the retail chainâsname on the 8,000 units. This machine would cost $16,000. PolaskiCompany has no assurance that the retail chain will purchaseadditional units in the future. Determine the impact on profitsnext year if this special order is accepted.
2. Refer to the original data. Assume again that Polaski Companyexpects to sell only 26,000 Rets through regular channels nextyear. The U.S. Army would like to make a one-time-only purchase of8,000 Rets. The Army would pay a fixed fee of $1.20 per Ret, and itwould reimburse Polaski Company for all costs of production(variable and fixed) associated with the units. Because the armywould pick up the Rets with its own trucks, there would be novariable selling expenses associated with this order. If PolaskiCompany accepts the order, by how much will profits increase ordecrease for the year?
3. Assume the same situation as that described in (2) above,except that the company expects to sell 34,000 Rets through regularchannels next year. Thus, accepting the U.S. Armyâs order wouldrequire giving up regular sales of 8,000 Rets. If the Armyâs orderis accepted, by how much will profits increase or decrease fromwhat they would be if the 8,000 Rets were sold through regularchannels?
Looking for correct answer to questions 2 and 3.
