[Math] 1條 linear programming assignment

XM8

PaperMart recycles uncoated paper (UP) and coated paper (CP) into recycled uncoated paper (RUP) and recycled coated paper (RCP).  The processing costs per ton of input are shown in the following table.
        To Produce
Use        RUP        RCP
UP        $1        $6
CP        $5        $3

The process using UP removes 15% of the input paper and leaves 85% of the input paper for recycled paper.  The process using CP removes 10% of the input paper leaves 90% of the input paper for recycled paper.

The purchase cost and availability for each type of paper are shown in the following table.
        Purchase Cost per ton of input        Availability in tons
UP        $8        350
CP        $9        300

To meet demand, PaperMart must produce at least 300 tons of RUP and at least 150 tons of RCP.

(a)        Formulate a linear programming model for PaperMart with the objective of minimizing the total cost.  (No need to solve)                                                (34 marks)

(b)        Suppose that RCP can also be produced by RUP, the processing cost is $4 per ton and the process using RUP also removes 20% of the input paper.  Modify the linear programming model in part (a).  [Hints: Add one decision variable,   to represent the tons of RUP used to produce RCP]

Part (a) 諗左好耐 應該點SET好 total 有4個variable ?  同埋唔係好明 percentage 果part 講咩

XM8

B PART 打漏野   [Hints: Add one decision variable, X rup - rcp to represent the tons of RUP used to produce RCP]

lth927

percentage 果part 係話整再造紙會令原本的紙有損耗, 個percentage係剩返可用的
(3*0.9 *rcp) + (5*0.9 * rup) <= 300    細過或等於300ton之前
(3*0.9 * 9 * rcp) + (5*0.9 * 9* rup) > 300 大過300ton之後要買紙, 所以要乘返買紙cost

(1* 0.85 * rup) + (6*0.85 *rcp) <=350   
(1* 0.85 *8* rup) + (6*0.85 *8*rcp) >350

(rup - 300) + (rcp - 150) = rup + rcp - 450
條式應該係咁列, 最後個條唔太肯定