Final Exam

Problem $6-07$

Problem $6-06$

Problem $9-07($Algorithmic$)$

Problem $9-22($Algorithmic$)$

Progress:$2/4$ items

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Problem $6-06$

Klein Chemicals, Inc., produces a special oil$-$based material that is currently in short supply. Four of Klein$$s customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein$$s management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant$$customer alternative:

Customer

Plant D$1$ D$2$ D$3$ D$4$

Clifton Springs $$32$ $$34$ $$32$ $$40$

Danville $$34$ $$30$ $$28$ $$38$

The plant capacities and customer orders are as follows:

Plant Capacity $($units$)$ Distributor Orders $($units$)$

Clifton Springs $5000$ D$12000$

D$25000$

Danville $3000$ D$33000$

D$42000$

How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Choose correct network model and Show linear programming formulation. If the constant is $"1"$ it must be entered in the box. If your answer is zero, enter $"0".$

Note: Dummy origin has supply of $4000.$

$($i$)($ii$)$

$($iii$)($iv$)$

Model $($iii$)$

Let xij $=$ amount of units produced by plant node i for customer node j$.$

Max fill in the blank $2$

$32$

x$11+$ fill in the blank $3$

$34$

x$12+$ fill in the blank $4$

$32$

x$13+$ fill in the blank $5$

$40$

x$14+$ fill in the blank $6$

$34$

x$21+$ fill in the blank $7$

$30$

x$22+$ fill in the blank $8$

$28$

x$23$

$+$ fill in the blank $9$

x$24+$ fill in the blank $10$

x$31+$ fill in the blank $11$

x$32+$ fill in the blank $12$

x$33+$ fill in the blank $13$

x$34$

s$.$t$.$ fill in the blank $14$

x$11+$ fill in the blank $15$

x$12+$ fill in the blank $16$

x$13+$ fill in the blank $17$

x$14<=$ fill in the blank $18$

$5,000$

fill in the blank $19$

x$21+$ fill in the blank $20$

x$22+$ fill in the blank $21$

x$23+$ fill in the blank $22$

x$24<=$ fill in the blank $23$

$3,000$

fill in the blank $24$

x$31+$ fill in the blank $25$

x$32+$ fill in the blank $26$

x$33+$ fill in the blank $27$

x$34<=$ fill in the blank $28$

Dummy

fill in the blank $29$

x$11+$ fill in the blank $30$

x$21+$ fill in the blank $31$

x$31=$ fill in the blank $32$

fill in the blank $33$

x$12+$ fill in the blank $34$

x$22+$ fill in the blank $35$

x$32=$ fill in the blank $36$

fill in the blank $37$

x$13+$ fill in the blank $38$

x$23+$ fill in the blank $39$

x$33=$ fill in the blank $40$

fill in the blank $41$

x$14+$ fill in the blank $42$

x$24+$ fill in the blank $43$

x$34=$ fill in the blank $44$

xij $>=0$ for all i$,$ j

Units Cost, $

Clifton Springs $-$ D$1$ fill in the blank $45$

$2,000$

fill in the blank $46$

Clifton Springs $-$ D$2$ fill in the blank $47$

$5,000$

fill in the blank $48$

Clifton Springs $-$ D$3$ fill in the blank $49$

$3,000$

fill in the blank $50$

Clifton Springs $-$ D$4$ fill in the blank $51$

$2,000$

fill in the blank $52$

Danville $-$ D$1$ fill in the blank $53$

fill in the blank $54$

Danville $-$ D$2$ fill in the blank $55$

fill in the blank $56$

Danville $-$ D$3$ fill in the blank $57$

fill in the blank $58$

Danville $-$ D$4$ fill in the blank $59$

fill in the blank $60$

Dummy $-$ D$1$ fill in the blank $61$

fill in the blank $62$

Dummy $-$ D$2$ fill in the blank $63$

fill in the blank $64$

Dummy $-$ D$3$ fill in the blank $65$

fill in the blank $66$

Dummy $-$ D$4$ fill in the blank $67$

fill in the blank $68$

Total Cost fill in the blank $69$

demand has a shortfall of

$.$

demand of

is not satisfied.

F