A company had the following purchases and sales during its first month of operations: January 1 Purchased 10 units at $4.00 per
1 answer:
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Answer:
i) Z = 20( 80 ) + 50(20 ) = $2600
ii) $3000
Explanation:
representing products A and B as x₁ and x₂
using the given data
Max ( z ) = 20x₁ + 50x₂ ( optimal product mix for optimal profit ) ---- ( 1 )
0.8 ( x₁ + x₂ ) ≥ 0
0.8x₁ + 0.8x₂ ≥ 0 ------------ ( 2 )
also x₁ ≤ 100 --- ( 3 ) considering the amount to be sold ( sales volume )
based on the availability of raw material
2x₁ + 4x₂ ≤ 240 ----- ( 4 )
resolve equations 2, 3, and 4 graphically
x₁ = 80 units , x₂ = 20 units
back to equation 1
Z = 20( 80 ) + 50(20 )
= 1600 + 1000 = $2600
ii) To increase the number of units of A produced
given that x₁ ≤ 100 and the actual optimal units produced = 80 units
2600 + 20(100-80)
= 2600 + 20(20) = 2600 + 400 = $3000
