9514 1404 393
Step-by-step explanation:
(a) Keep in mind the meaning of the variables:
- x = PS4 units sold
- y = X.box 1 units sold
With these definitions in mind, we can examine the constraints.
x ≥ 0 . . . . . we cannot sell a negative number of PS4 units
y ≥ 0 . . . . . we cannot sell a negative number of X.box 1 units
y ≥ 5 . . . . . we intend to sell at least 5 X.box 1 units
y ≤ 10 . . . . we cannot sell more than 10 X.box 1 units
x + y ≤ 10 . . . . . we can sell at most 10 units total
(Please note that the constraints y ≥ 0 and y ≤ 10 are redundant to other more restrictive conditions.)
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(b) The objective function tells us the total profit:
P(x, y) = 100x + 80y
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(c) Juan's goal: P(2, 7) = 100(2) +80(7) = 200 +560 = 760
Justin's goal: P(4, 5) = 100(4) +80(5) = 400 +400 = 800
Meeting Justin's goal would result in more profit.
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(d) It is not possible to sell a negative number of units*, so negative values for the variables do not make any sense. (This is consistent with the x≥0, y≥0 constraints above.)
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* Some linear programming problems plan for a certain number of returned items. Those could be considered to be negative sales.