Question 2: In the model for backorders, replace the backorder cost per unit and time unit, b1, by a backorder cost per unit, b2. This means that there is no difference between long and short delays. Show that for a given 0x1 the optimal costs can be expressed as: c=2Adh(1x)+b2dx. Relevant textbook section below: In E4. (4.15) we we thas the ralio of time with poithe iook is (tx) and with backoelen x. When the imentoy level in pouinive. the aumpe toxk on hand in Q(13)2, bat when the imentoy level is asgative, the weck ce hasd is aefa So: we otkain the anerge ibock co land as (1x)Q(x)2+x0=Qix)/2. in compleve atalozy the averape munter of hodondes is 0x2/2 The cont is cones in x, and it is easy to see that the optinal x is indefeolem of Q. Hy seting the derivalive equal to acro se olitaia by the demand of is the avsrage waiting tine per unit demumbed. Tis relationdip is See alwe Sect. 10.2. Similarby, the merage imentoy be hand diviled by d is the average waiting time for a and to be demandet. A Howing barkorders means that wone niti are delivened in sack afte they have. beci demanded. Let us define I= fraction of demsed that is baclardered. This means that when a bakch Q is delneed the fretioe x of the buch it ued io: cover beckonders ihat have accured before the tokch was delivered Wis wial io queimine boik x and 0 . The develepent of the insntury level is very similar to that in Fing. 4.1. Soe Fige 4.4. The cost are now olrained au: c=2Q(tx)2b+2Q2bi+QdA