Winston #27 683m50

PROBLEM: Grummins Engine produces diesel trucks. New government emission standards have dictated that the average pollution emissions of all trucks produced in the next three years cannot exceed 10 grams per truck. Grummins produces two types of trucks. Each type 1 truck sells for $20,000, cost $15,000 to manufacture, and emits 15 grams of pollution. Each type 2 sells for $17,000, cost $14,000 to manufacture, and emits 5 grams of pollution. Production capacity limits total truck production during each year to at most 320 trucks. Grummins knows that the maximum number of ach truck type that can be sold during each of the next years is given in Table 62. Demand can be met from previous production or the current year’s production. It costs $2,000 to hold 1 truck (of any type) in inventory for one year. TABLE 62 Year 1 2 3

Type 1 100 200 300

Type 2 200 100 150

Decision variables: Let:

xij

be the number of diesel trucks to be produced of type i on year j

yij

be the number of diesel trucks to be sold of type i on year j

wij

be the ending inventory at year j of diesel truck type

Objective function:

Max z(profit)=

20,000 y 1 j−15 , 000 x1 j+ 17,000 y 2 j (¿−14,000 x 2 j ) 3

∑¿ j=1

Constraints: YEARLY PRODUCTION CONSTRAINTS x 11 + x 21 ≤320 x 12+ x 22 ≤ 320 x 13+ x 23 ≤ 320 DIESEL TRUCK TYPE 1 DEMAND CONSTRAINTS w 11=x 11−100 w 12=x 12 +w 11−200 w 13=x13 +w 12−300 DIESEL TRUCK TYPE 2 DEMAND CONSTRAINTS w 21=x 21−200 w 22=x 22 +w 21−100 w 23=x23 +w 22−150 POLLUTION CONSTRAINT x1 j x2 j 3

3

2

∑ ¿ ≤ 10 ∑ ∑ xij j=1

j=1 i=1

¿

3

∑ ¿+5 ¿ j=1

15 ¿