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Answer:
Explanation:
The <em>profit</em> will be the revenue less the cost.
The revenue will be the price times the number of items sold. <em>The price is $40 the piece</em>. Work with a piece.
- Revenue = $40
The total cost of a piece is the sum of the <em>cost of the supplies</em>, the s<em>eller's fees</em> and the <em>shipping costs</em> of a piece:
- Cost of supplies: $8.00
- Seller's fee: 9% of $40 = 0.09 × $40 = $3.60
- Shipping costs: $2.00
- Total cost = $8 + $3.60 + $2 = $13.60
Profit = Revenue - Cost = $40 - $13.60 = $26.40
To find the <em>hourly profit</em> you must divide the profit of a piece by the <em>hours of labor</em> to make a piece.
- Hourly profit = $26.40/1.5hour = $17.60/hour
The objective function Z = 2x + 3y cannot be maximized, while the maximum value of the objective function Z = 2x + 5y is 19
<h3>Part A (Question 1): Maximize Z</h3>The objective function is given as:
Z = 2x + 3y
The constraints are given as:
3x+2y≤15
4x+y≤0
x≥0; y≥0
See attachment for the graph of the constraints
From the attached graph, we have the optimal solution to be:
(x,y) = (-3,12)
Because x≥0 & y≥0, and x is negative in (-3,12), then
The function cannot be maximized.
<h3>Part B (Question 7): Maximize Z</h3>The objective function is given as:
Z = 2x + 5y
The constraints are given as:
x + y ≤ 5
y - x ≤ 1
x≥0; y≥0
See attachment for the graph of the constraints
From the attached graph, we have the optimal solution to be:
(x,y) = (2,3)
Substitute 2 and 3 for x and y in the objective function.
Z = 2 * 2 + 5 * 3
Evaluate
Z = 19
Hence, the maximum value of the objective function is 19
The questions 21, 22, 23 and 25 are not included in the attachment
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