Can anybody help? A manufacturing company makes two types of water skis, a trick

Question

Can anybody help?

A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. (A) If the profit on a trick ski is $30 and the profit on a stator ski is $50, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ The maximum occurs when trick skis and slalom skis are produced (B) Discuss the effect on the production scheduled and the maximum profit if the profit on a slalom skis are produced. The maximum profit $. The maximum occurs when trick skis and slalom skis are produced (C) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $60. The maximum profit $. The maximum occurs when trick skis and slalom skis are produced.

Explanation / Answer

Solution:

Let x unit of trick ski and y unit of slao is being produced

Maximize p = 30x + 50y subject to
5x + 4y <= 160
x + y <= 35

using simplex method for

Tableau #1
x y s1 s2 p   
5 4 1 0 0 160
1 1 0 1 0 35   
-30 -50 0 0 1 0

Tableau #2
x y s1 s2 p   
1 0 1 -4 0 20   
1 1 0 1 0 35   
20 0 0 50 1 1750   

therefore optium soulition:

Optimal Solution: p = 1750; x = 0, y = 35

Answer: the maximum profit $ 1750 the maximum occours when 0 trick skis and 35 slalom skis are produced

Now for

if profit decreses on a slalom skie decreases to $ 35

then

Maximize p = 30x + 35y subject to
5x + 4y <= 160
x + y <= 35

using simplex method

Tableau #1
x y s1 s2 p   
5 4 1 0 0 160
1 1 0 1 0 35   
-30 -35 0 0 1 0

Tableau #2
x y s1 s2 p   
1 0 1 -4 0 20   
1 1 0 1 0 35   
5 0 0 35 1 1225   

Optimal Solution: p = 1225; x = 0, y = 35

Answer: the maximum profit $ 1225 the maximum occours when 0 trick skis and 35 slalom skis are produced

Now again

if slalom increases to $ 60

then

Maximize p = 30x + 60y subject to
5x + 4y <= 160
x + y <= 35

using simplex method

Tableau #1
x y s1 s2 p   
5 4 1 0 0 160
1 1 0 1 0 35   
-30 -60 0 0 1 0

Tableau #2
x y s1 s2 p   
1 0 1 -4 0 20   
1 1 0 1 0 35   
30 0 0 60 1 2100   

Optimal Solution: p = 2100; x = 0, y = 35

Answer: the maximum profit $ 2100 the maximum occours when 0 trick skis and 35 slalom skis are produced

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