Ace Novelty Wishes to Produce Two Types of Souvenirs: Type

question 38

Short Answer

Ace Novelty wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1.00, and each type-B souvenir will result in a profit of $1.20. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II. There are 3 hours available on machine I and 5 hours available on machine II for processing the order.
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Let x be the number of type-A souvenirs and y be the number of type-B souvenirs to be made. Then the problem can be reduced to a linear programming problem with the objective function P = x + 1.2y and constraints
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Please enter your answers to two decimal places.
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Find the contribution to the profit of a type-B souvenir for which the optimal solution holds.
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$ ≤ c _type-B ≤ $
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What will be the optimal profit of the company if the contribution to the profit of a type-A souvenir is $1.90 (with the contribution to the profit of a type-B souvenir held at $1.20)?
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$ __________
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What will be the optimal profit of the company if the contribution to the profit of a type-B souvenir is $2.80 (with the contribution to the profit of a type-A souvenir held at $1.00)?
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$ __________

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Definitions:

Price Of Factor

The cost associated with a factor of production, such as labor or capital, used in the creation of goods or services.

Output Supply

The total amount of a product or service that is available for purchase at any given price level in a given market.

Long-Run Cost Function

A concept that describes how the total production costs of a firm change based on output levels, considering all inputs as variable in the long term.

Output Supply

The total amount of a good or service that producers are willing and able to sell at a given price over a certain period of time.