CHP3&4HW/DQ
Chapter3&4
Chapter3
Parta (statistical part)
Theminimum cost incurred in shipping from warehouses 1,2,3 to retailoutlet 1,2,3 is $4,370.This cost is reached when zero units areshipped from warehouse 1 and 2 to retail outlet 1 and 2,145 unitsfrom warehouse 1 to outlet 3,30 units from warehouse 2 to outlet 1,zero units from warehouse 2 to outlet 2, 140 units from warehouse 2to outlet 3 ,180 units from warehouse 3 to outlet 1, 90 units fromwarehouse 3 to outlet 2 and zero units from warehouse 3 to outlet 3.
Basedon the logistic model, there is underutilization of the availablespace in the warehouse which can be used for other purposes, it isalso clear that at a particular time of transportation the loadedtrucks are not full. The improvement can therefore be made in thewarehouse utilization and the transportation trucks. There are noexcess supply since all supply from warehouse 1 was shipped toretail outlet 3 whereas all supply from warehouse 2 was shipped tooutlet 1 and 3 and all from warehouse 3 was shipped to outlet 1 withno surplus.
Therewas no shortages since all the demand by retail outlet 1 was met bywarehouse 2 and 3 whereas retail outlet 2 was supplied by warehouse 3and retail outlet 3 got its supply from warehouse 1 and 2.Hence noshortages.
Thesolver output implies that no units should be shipped from warehouse1 to retail outlet 1, warehouse 1 to retail outlet 2, warehouse 2 toretail outlet 2, and from warehouse 3 to retail outlet 3. It alsoimplies that if that is done, the logistic cost will be $4,370.
Thekey assumptions made are as follows:

The decision variable assumes nonnegative values.

We assume that any change in the constraint inequalities will have the proportional change in the objective function.

The total least cost of the objective function is determined by the sum of product contributed by each product separately.
Inthe Sensitivity analysis, the shadow price column, it informs us byhow much our cost would change if we had more of a particularresource.
Theshadow price for Demand at outlet 3 is high followed by demand atoutlet 2 and then at outlet 1.Therefore our cost would change if weimproved on the demand.
Formore feasible solution, it is advisable to include more variableswhich will result in the minimum cost for shipping. Delivery timesshould be considered so that at a particular time a truck can carryunits from one warehouse to two different outlets.
Partb (business part)
Question8
Thelaw of demandstatesthat an increase in demand results to an increase in the price andvice versa. However this law holds when other factors are keptconstant. The theory also holds for normal goods and therefore,contraction between the theory and the facts may exist for inferiorand luxury goods. For instance, despite of the fallen demand oflongplaying record technology, the product is still selling in themarket and even at higher prices. This signifies that the law ofdemand does not hold for LP and this could be due to uncontrollablefactors. These factors may include consumers switching cost,bureaucracies and status quo within organization of the users of LPtechnology among other factors. The apparent contraction between theeconomic theory and the facts may also exist where the firm desiresto maintain and adhere to the set revenue goals. If this is the casethe firm will have to set higher prices at low demand to maintaintheir revenue targets.
Question10
Parta)
Q=15004P+5A+10I+3PxP=420A=20,000I=15,000Px=500Q=15004xP(400)=5(20)"Dropthe 000"Q=154(420)+5(20)+10(15)+3(500)
Q=15001680+100+150+1500
Q=1570
Therefore,the quantity demanded Q under this scenario is 1,570units.
Partb) ChangingPxto 400
Q=15004P+5A+10I+3PxP=420A=20,000I=15,000Px=400Q=15004xP(420)=5(20)"Dropthe 000"Q=154(400)+5(20)+10(15)+3(400)
Q=15001680+100+150+1200
Q=1,120
Thisimplies that the firm will sell less and to counteract the drop theadvertising expense can be adjusted as follows
1570=154(420)+ 5(A)+10(15)+3(400)
1570=15001680+5A+150+1200
1570=1170+ 5A
400=5A
A=80
Therefore,Advertising needs to be increased by $60,000 to maintain the demand.
Decisionevaluation
Declinein revenue (15701170)*400=160,000
Lessthe decision to increase advertising expense is worth since the firmwill achieve higher profitability by maintaining the demand.
Partc) Other factors to be considered
Theother factors to be considered will include the following
Marginalcost, customer royalty, product life cycle, consumers’ bargainingpowers, and product differentiation among others.
Forexample, if the product is at the declining stage, investing more ininvestment could be of no help to the firm. Similarly, if theproducts of the firm are highly differentiated, a reduction in theprice of the competitors’ product could have no impact to demand inthe travel company.
Question12
Q= 100P^{0.3}
Thedemand equation above is an exponential function. The functionindicates a negative, nonlinear slope as indicated in the demandcurve below the demand curve is known as exponential demand curve.
Exponentialdemand curve signifies that demand increases with a decrease in pricebut at a decreasing rate.
Chapter4
Question2
Q= 20 – 2P
Atprice 5
Q= 20 – 2(5) = 10
Atprice 9
Q= 20 – 2(9) = 2
Ep=
Partb)
Atprice 5
Q= 20 – 2(5) = 10
Atprice 6
Q= 20 – 2(6) = 8
Ep= 2
Partc)
Q= 20 – 2P
Revenue= Q*P
R=20P– 2P^{2}
=at maximum revenue
dR/dP= 0
204P=0=> 5=5
Therefore,at price of %, a change in quantity has no effect on revenue becauseat this price level we have the maximum revenue.
Question4
Q=10011P+0.6Y
Interpretthe equation. parta) Interpreting the equation
Theequation above signifies that the quantity produced depends on price(P) and the income Y. the quantity produced is inversely proportionalto price and directly proportional to the income.
partb)
Q=10011P+0.6YP=7,Y=50,

Q=10011(7)+0.6(50),
Q=10077+30
Q=53Units
Ep+dQ/dPP/Q =(11)(7/53)
Ep=1.45
c). EY= dQ/dY(Y/Q)
=0.6(50/53)EY=0.57 Question10)
Q= 1450 – 190P
Elasticity 

P 
Q 
Point 
Arc 
Total revenue 
Marginal revenue 
7.00 
120.00 
– 
– 
840.00 
– 
6.50 
215.00 
– 0.01 
– 190.00 
1,397.50 
557.50 
6.00 
310.00 
– 0.01 
– 190.00 
1,860.00 
462.50 
5.50 
405.00 
– 0.01 
– 190.00 
2,227.50 
367.50 
5.00 
500.00 
– 0.01 
– 190.00 
2,500.00 
272.50 
4.50 
595.00 
– 0.01 
– 190.00 
2,677.50 
177.50 
4.00 
690.00 
– 0.01 
– 190.00 
2,760.00 
82.50 
3.50 
785.00 
– 0.01 
– 190.00 
2,747.50 
– 12.50 
3.00 
880.00 
– 0.01 
– 190.00 
2,640.00 
– 107.50 
2.50 
975.00 
– 0.01 
– 190.00 
2,437.50 
– 202.50 
References
Keat,P.G., Young, P.K.Y. & Erfle, S.E. (2013). Managerial Economics(7th edition).Upper SaddleRiver, NJ: Pearson Prentice Hall.