the equetion needed is in the privious question Hamilton Co. is a manufacturer o
ID: 443366 • Letter: T
Question
the equetion needed is in the privious question
Hamilton Co. is a manufacturer of pool care equipment. Hamilton has just introduced a new product for pool cleaning. Each unit costs $160 to manufacturer, and the introductory price is set to be $210. At this price, the forecasted demand is normally distributed with a mean of 100 and a standard deviation of 40 for the next summer season. Any unsold units at the end of the summer season are unlikely to be valuable and will be disposed of in a post-season sale for $40 each. It costs $30 to hold a unit in inventory for the entire season. How many units should Hamilton manufacture for sale? What is the expected profit for the season? (Use the formula provided in the corrected question 1) Let p denote the unit selling price, r the unit purchase cost, and v the unit salvage revenue, with no loss-of-goodwill cost. Let f(x; mu, sigma) denote the probability distribution function for a normally distributed random variable with mean of m and standard deviation o. and F(x; mu, sigma) the cumulative distribution function. Show that when demand is normally distributed with a mean of m and a standard deviation of s the expected profit for a single period newsvendor model is given by P(q) = (p - v)mF(q - m/s; 0, 1) - (p - v) sf(q - m/s); 0, 1 - q(c - v)F(q: m, s) + q(p - c) For a normally distributed random variable with mean mu and standard deviation sigma.Explanation / Answer
a) Manufacturer produce the units for sale
Estimating 8 weeks considered for Summer
Mean Demand = 8+1 * 40
=360 units
Standard devaiation of demand over l+ 1 weeks is = 8 + 1 * 40
=120 units
We can take S.D Demand = 120 units is manufacturer is ready to produce for sale because it is least units.
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b)p(q) =(210- 40)mF(120-100/40) - (210 - 40 ) sf(120-100/40) -120(160-40)F+120(210-160) * (1-(f)
=170mF (0.50) - (170)sf(0.50) -14400 * -1
= 0 - 14400 * -1
= -14,400 * -1
=$14,400 expected profit
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