1. Quackers Toys Inc., manufactures two types of radio operated trucks: Model X and Model Y....

1. Quackers Toys Inc., manufactures two types of radio operated trucks: Model X and Model Y. Both models require metal frame parts and electrical components. The shop manager estimates that there will be 200 units of frame parts and 300 units of electrical components available for production next week. Each Model X requires one unit of frame parts and two units of electrical components. Each Model Y requires three units of frame parts and two units of electrical components. The company can sell as many trucks as it produces at the prevailing market prices of $120 for each Model X and $90 for each Model Y. Materials and labor costs total $40 for each Model X and $30 for each Model Y. Model X appears to be the hot model for this year’s holiday rush so the company wants to produce twice as many model X as model Y.

Write the linear programming formulation to help Quackers determine how many units of each product the company should produce to maximize total dollar profit.

Solutions

Expert Solution

Decision variables:

x = Number of model X produced

y = Number of model Y produced

z = Profit ($)

Objective function:

Total revenue = 120x + 90y and total cost = 40x + 30y

Profit = 120x + 90y – (40x + 30y) = 80x + 60y

Maximize z = 80x + 60y

Constraints:

x + 3y ≤ 200 [Frame parts]

2x + 2y ≤ 300 [Electrical components]

x = 2y [Production]

x, y ≥ 0 and integers

Solver model and solution:

Optimal solution: x = 80, y = 40, z = 8800

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orchestra answered 1 year ago

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