A company produces two products, A and B. The sales volume for A is at least 80% of the total salces for both A and B. However, the company cannot sell more than 100 units of A per day. Both products use one raw material, of which the maximum daily availability is 240 lb. The usage rater of the raw material are 2lb per unit of A and 4 lb per unit of B. The profit units for A and B are $20 and $50, repectively. Set this problem up as a linear program to determine the optimal product mix for the company. Then solve using excel. Next, answer the following questions: 1. How much should the company be willing to pay to increase the number of units of A that it can sell

Question

contestada

Respuesta :

batolisis batolisis · Answer 1 · 2021-06-14T13:22:55+02:00

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