This is the app page of ODMO program for Meet the demand of production in the penalty minimization

A manufacturer produces two types of products with the labels X and Y with the information given in the following table. The target of this manufacturer weekly is to achieve a profit of $ with $1 penalty for each dollar lower than the target. There are hours of available labor required to be used efficiently. Due to industrial law, the manufacturer incurs a $2 penalty for each hour of overtime. Meanwhile, for each hour of unused labor, a $1 penalty is incurred. There is an order of at least units of product X and units of product Y. If the product quantity is lower than the requirement, there is a $2 penalty for each unit lower.
How many products each type does the manufacturer need to produce to minimize the penalty?

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