What is the minimum value of the objective function, C with given constraints? C=5x+3y {⎨x+3y≤9 {5x+2y≤20 {x≥1 {y≥2
1 answer:
Answer:
The answer is below
Step-by-step explanation:
Plotting the following constraints using the online geogebra graphing tool:
x + 3y ≤ 9 (1)
5x + 2y ≤ 20 (2)
x≥1 and y≥2 (3)
From the graph plot, the solution to the constraint is A(1, 2), B(1, 2.67) and C(3, 2).
We need to minimize the objective function C = 5x + 3y. Therefore:
At point A(1, 2): C = 5(1) + 3(2) = 11
At point B(1, 2.67): C = 5(1) + 3(2.67) = 13
At point C(3, 2): C = 5(3) + 3(2) = 21
Therefore the minimum value of the objective function C = 5x + 3y is at point A(1, 2) which gives a minimum value of 11.
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Answer:
Last week her sales were <u>$4500</u>.
Step-by-step explanation:
Given:
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.
She also earns a base salary of $750 per week.
Her total earnings for the week were $1,076.25.
Now, to find her sales last week.
Let the sales of last week be
Base salary = $750.
Total earnings = $1076.25.
So, we deduct the base salary from the total earnings first:
Thus, the rest of the earnings is $326.25 which is the 7.25% commission on sales.
Now, to get the sales of last week we put an equation:
<em>Multiplying both sides by 100 we get:</em>
<em>Dividing both sides by 7.25 we get:</em>
The sales of last week = $4500.
Therefore, last week her sales were $4500.