High School

The PSV toy factory makes two types of toy cars, type X and type Y. Daily orders require at least 100 units of type X and at least 90 units of type Y. It takes 1.5 man-hours to make a type Y car. The staff can work no more than 360 man-hours per day.

How many units of each type should be produced to maximize the profit if a unit of type X gives 80 and a unit of type Y gives 74 profit?

Answer :

The PSV Toy Factory should produce 100 units of type X and 240 units of type Y.

Let's define variables: x = number of type X toy cars produced and y = number of type Y toy cars produced.

  • Constraints -

Daily orders for type X: x ≥ 100

Daily orders for type Y: y ≥ 90

Man-hours constraint: 1.5y ≤ 360

  • Simplifying the man-hours constraint: y ≤ 240

  • Objective Function

We need to maximize the profit function:

Profit = 80x + 74y

  • Considering the constraints, the feasible region for (x, y) is:

x ≥ 100

90 ≤ y ≤ 240

  • Let's evaluate the profit at different points within the feasible region:

At (x = 100, y = 90): Profit = 80(100) + 74(90) = 8000 + 6660 = 14660

At (x = 100, y = 240): Profit = 80(100) + 74(240) = 8000 + 17760 = 25760

At (x = 100, y = 240) produces the highest profit.

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