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

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

answer; purpose nondisclosure;