finite math- PLEASE help with both parts and i will rate! thank you! solve this

Question

finite math- PLEASE help with both parts and i will rate! thank you!

solve this problem using the simplex method. A company manufactures checker sets and chess sets. Suppose each day the company has available 1600 boards (which can be used for both games) and 80,000 units of wood for making pieces. Each checker set uses 20 units of wood and each chess set uses 60 units of wood. The distributors the company sells to can take up to 1250 checker sets per day and up to 750 chess sets per day. The company makes a profit of $1.00 on each checker set and $2.00 on each chess set. (a) How many checker sets and how many chess sets should the company make each day in order to maximize its profits? checker sets chess sets (b) What is the profit per day using this strategy? per day

Explanation / Answer

a)let number of checker sets are X and chess set are Y

hence X+Y=1600

and 20X+60Y =80000

X<1250 and Y<750

need to maximize X+2Y

solving above will give

number of checker board X=850

and number of chess boards Y=750

also profit =2350

2) let corn acres =X, Soybean Acres =Y

X+Y=480

60X+40Y=19200

and 50X+100Y=20000

we need to maximize profit which is equal to 60X+90Y

hence solving above

corn area X =280

soy bean area Y =60

and profit =22200

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