Question

The Toys-R-4-U Company has developed two new toys for possible

inclusion in its product line for the upcoming Christmas season. Setting up the production

facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. The toys

would generate a unit profit of $10 for toy 1 and $15 for toy 2.

The company has two factories that are capable of producing these toys. However, to

avoid doubling the start-up costs, just one factory would be used for producing these toys,

where the choice would be based on maximizing profit. Toy 1 can be produced at the rate of

50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of

40 per hour in factory 1 and 25 per hour in factory 2. Factories 1 and 2, respectively, have

800 hours and 700 hours of production time available before Christmas that could be used

to produce these toys.

The problem is to determine how many units (if any) of each new toy should be produced

before Christmas to maximize the total profit.

(a) Formulate an MIP model for this problem

(b) Use Python to solve this problem.

Answer 1

Given,

Unit cost Toy-1 = $10

Unit cost Toy-2 = $15

Fixed cost Toy-1 =$50,000

Fixed cost Toy-2 =$80,000