A company manufactures two products A and B. The unit revenues are $2 and $3 res

Question

A company manufactures two products A and B. The unit revenues are $2 and $3 respectively. Two raw materials (M1 and M2) used in manufacture of the two products have daily availabilities of 18 and 28 units respectively. One unit of A uses 2 units of Ml and 2 units of M2, and 1 unit of B uses 3 units of M1 and 6 units of M2. a) Determine the shadow prices of M1 and M2 b) Suppose that 4 additional units of M1 can be acquired at the cost of 30 cents per unit. Would you recommend the additional purchase? c) If M2 availability is increased by 5 units, determine the associated optimum revenue d) What is the most value the company should pay per unit of M2?

Explanation / Answer

solution:

(a) dual price of M1 & M2

for product A 2M1+2M2=$2

and product B 3M1+6M2=$ 3

then M1=$1 and M2 = $1

(B) yess if 4 units of M1 is availbale for 30 cents per unit then we shoul purcahse this because it's cheaper.

(C) most the company should pay per unit of M2 = $1

(D) available units of M1 =18 units

then production of product A & B is possible in ration 2:3 as required material =3.5 units & 4.8 Units respectively

available units of M2 = 28 units

then production of product A & B is possible in ratio 2:6 as required material =4.5 units & 13.5 Units respectively

optimum revenue product A= 3.5*2=$7

optimum revenue product B=4.8*3=$14.4

because of limited availability of material M1

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