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BEN 65 Producton Plariwg aw Sckedulgg 13_ An automotive warehouse stocks & variety of parts that are sold at neighborhood stores: One particular part; popular b...

Question

BEN 65 Producton Plariwg aw Sckedulgg 13_ An automotive warehouse stocks & variety of parts that are sold at neighborhood stores: One particular part; popular brand of oil filter; is purchased by the warehouse for $1.SO each: It is estimated that the cost of order processing and receipt is SIO per order: The company uses an inventory carrying charge based on a 28 percent annual interest rate. The monthly demand for the filter follows normal distribution with mean 280 and standard deviation 7

BEN 65 Producton Plariwg aw Sckedulgg 13_ An automotive warehouse stocks & variety of parts that are sold at neighborhood stores: One particular part; popular brand of oil filter; is purchased by the warehouse for $1.SO each: It is estimated that the cost of order processing and receipt is SIO per order: The company uses an inventory carrying charge based on a 28 percent annual interest rate. The monthly demand for the filter follows normal distribution with mean 280 and standard deviation 77. Order lead time is assumed t0 be five months_ Assume that ifa filter is demanded when the warehouse is out of stock; then the demand is back-ordered and the cost assessed for each back-ordered demand is S12.80_ Determine the following quantities: The optimal values of the order quantity and the reorder level: b. The average annual cost of holding; setup. and stock-out associated with this Item assuming that an optimal policy is used. Evaluate the cost of uncertainty for this process. That is. compare the average annual cost YOu obtained in part (b) with the average annual cost that would be incurred if the lead time demand had zero variance 16. Suppose that in Problem 13 the stock-out cost is replaced with a Type service objective of 95 percent: Find the optimal values of (Q, R) in this case. 17. Suppose that in Problem [3 a Type 2 service objective of 95 percent is substituted for the stock-out cost of $12.80. Find the resulting values of Q and R. Also. what is the imputed cost of shortage for this case?



Answers

Assume the following cost data are for a purely competitive producer: $$\begin{array}{ccccc} \hline \begin{array}{c} \text { Total } \\ \text { Product } \end{array} & \begin{array}{c} \text { Average } \\ \text { Fixed cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Variable cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Total cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 \\ 1 & \$ 60.00 & \$ 45.00 & \$ 105.00 & \$ 45 \\ 2 & 30.00 & 42.50 & 72.50 & 40 \\ 3 & 20.00 & 40.00 & 60.00 & 35 \\ 4 & 15.00 & 37.50 & 52.50 & 30 \\ 5 & 12.00 & 37.00 & 49.00 & 35 \\ 6 & 10.00 & 37.50 & 47.50 & 40 \\ 7 & 8.57 & 38.57 & 47.14 & 45 \\ 8 & 7.50 & 40.63 & 48.13 & 55 \\ 9 & 6.67 & 43.33 & 50.00 & 65 \\ 10 & 6.00 & 46.50 & 52.50 & 75 \\ \hline \end{array}$$ a. At a product price of $\$ 56,$ will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? Explain. What economic profit or loss will the firm realize per unit of output? b. Answer the relevant questions of 4 a assuming product price is $\$ 41$ c. Answer the relevant questions of 4 a assuming product price is $\$ 32$ d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2 ) and indicate the profit or loss incurred at each output (column 3). $$\begin{array}{cccc} \hline \begin{array}{c}
\text { (1) } \\ \text { Price } \end{array} & \begin{array}{c} \text { (2) } \\ \text { Quantity } \\ \text { Supplied, } \\ \text { Single Firm } \end{array} & \begin{array}{c} \text { (3) } \\ \text { Profit }(+) \\ \text { or Loss }(-) \end{array} & \begin{array}{c} \text { (4) } \\ \text { Quantity } \\ \text { Supplied } \\ 1500 \text { Firms }
\end{array} \\ \hline \$ 26 & \text {_____} & \$ \text {_____} & \text {_____} \\ 32 & \text {_____} & \text {_____} & \text {_____} \\ 38 & \text {_____} & \text {_____} & \text {_____} \\ 41 & \text {_____} & \text {_____} &
\text {_____}\\ 46 & \text {_____} &
\text {_____} &
\text {_____} \\ 56 &
\text {_____} &
\text {_____} &
\text {_____} \\ 66 &
\text {_____} &
\text {_____} &
\text {_____} \\ \hline \end{array}$$ e. Explain: "That segment of a competitive firm's marginalcost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically. f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4). g. Suppose the market demand data for the product are as follows: $$\begin{array}{|cc|} \hline \text { Price } & \begin{array}{c} \text { Total Quantity } \\ \text { Demanded } \end{array} \\ \hline \$ 26 & 17,000 \\ 32 & 15,000 \\ 38 & 13,500 \\ 41 & 12,000 \\ 46 & 10,500 \\ 56 & 9500 \\ 66 & 8000 \\ \hline \end{array}$$ What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?

From number three party. So the order costs 16 times are carrying costs. It's gonna be four times X over to just two X. So then the total inventory costs is gonna be two x plus 16 are party order quantity multiplied by number of orders consist the total number of packages so that just b r times X, which is to go to 800. So we solve this constraint function for our ours Will Thio 800 or X substituting the equation. We got two X plus 1 to +800 over X and then take the derivative of this gives us two minus one to a 00 over X squared set this equal to zero to find extreme points we saw for X, we get access, you go to 80 and article 2 10. So therefore minimum inventory costs is gonna be 3 to 0

Alright problem before so order costs is 1. 60 are carrying costs 32 times x over to giving a 16 x so total inventory costs is gonna be 1 60 r plus 16 x part B order quantity times number of orders per year. Give us gives us our constraint function. Then sulfur are Plug this back in to our C and we get 10 to 400 over X plus 16 x modifying our extreme points. So we take the derivative 16 minus 10 to 400 x squared set this equal to zero get X equals 80 and then plug that back into the sea to find minimum inventory costs 256 year dollars.

In this problem. The percentage change in a rich market share Byron is given which be happy, noting the X for four tests cities at four control cities. In first caution, the had befriended me off the change in market ship for the fourth test cities. To find them me, we will require the summer fall X values for the best cities that this plus 18 plus 15 last seven blasting because it quite so 50. So our submission eggs for the Death Cities is 50 and therefore me expert is equal to summation X that this 50 divided by end which is four, and there are four test cities. So this is equal group 12.5 that this the mean off the change in market share for the four test cities is 12.5. In the next part, we have to find the mean off the changing market ship 44 control cities. For that be the required information x 44 control cities which is plus one minus eight minus pi plus zero, which is equal to minus 12 that this summation x 44 control cities is equal to minus 12 and therefore meaning equal to summation X that this minus trail divided by end that this four as there are four controlled cities So I mean is it will do minus three. That this the mean off the changing market shed for the four control cities is minus three. In the next part, we have to find a stand that aviation off the change in market ship for the best cities. For that to be very quiet X square and its summation. So we will find the square off each x value. It didn't square, is it? While you treat, drink before 15 square is to 25. So that square is 49 and that square this 100. So the sound off on X travel used the estimation X squared is it Will do 6 98. Now we first find debate yet 44 test cities by using the formula X ray s square required to summation X squared, which we have found to be well to 6 98 minus. And that this foot, my dear, like my ex Bob Square, that doesn't mean for the test cities which we have found to be well do 12.5. We have to take its square, so it will be well going. Five squid divided by n minus one as any well before. And my husband is four minus one. That this tree therefore variance est square is equal. Do grant before 0.33 Now, as little sent activation s is equal to another rude as square so s is equal to another mood drank before point 33 which is sick. Well, do four point name. Therefore the standard deviation off the change in market share for the test cities is four point name in the next question being asked if I understand that aviation off the changing market ship for the control cities. For that we define summation X script for the control cities. But square is one minus X squared is 64 minus five square is 25 and zero square is zero. So the square for X credible used the sum of all X squared venues that this summation X squared isn't going to do 90 Dimension X squared is equal. Dude, I d so as square. Is it going to summation X quit that this 90 minus and we just four my name like by ex script their ex My divide Rex Bath script When experienced in me for the controls it this which we have found to be quite so minus three. So it would be my nested e squid divided by end minus one. Our anything well before so n minus one is equal to three. Therefore, Radiance s squared is equal Do anything and so standard A nation s is equal to another route as square which is equal to another route 18 and it is a choir do four going to do that? This the standard deviation off the changing market ship for the control cities is 4.2 now in the next kosher it this asked to find them difference between it means off parks in and be the mean which we have found in part A is 12.5 as we have to take the difference. Well, it's a threat. Did me founding the part B This minus three. So we this object minus three. So this is it Will do. Do I find five? Blustery beach is equal to 15.5. That this the estimate off the post sex change in sales due to the pre mia is 15.5 now in the next part of this given dead. The two standard deviations, which we have found but used to calculate an editor off. Bless my nurse. 7.95 This this amount of better we have to find this more less and now just estimate off the increase in sales. The smallest has to make that this is the lowest estimate can be from by taking this estimate, which were found in Park E that this 15.5 minus dick Even better that this 7.95 So this is it will do 7.55 and the land just estimate or the highest estimate can be found by taking this 15.5 last 7.95 the Jessica want to 23 point full five, so this more less estimate is 7.55 And Villa just estimated 23.45


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