A Furniture Company Is Introducing a New Line of Executive

question 87

Multiple Choice

A furniture company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three models - A, B, and C - are to be marketed. Each model A desk requires hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model B desk requires hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model C desk requires hr, hr, and hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $34, the profit on each model B desk is $37, and the profit on each model C desk is $28. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is 279 hr, 181 hr, and 166 hr, respectively. To maximize company's profit, how many desks of each model should be made in the month? What is the largest profit the company can realize? Are there any resources left over?

• A) 60 units of model A, 76 units of model B, 60 units of model C; maximum profit $6,532; 0 hr left over in the fabrication department, 0 hr left over in the assembly department, 0 hr left over in the finishing department
• B) 60 units of model A, 60 units of model B, 76 units of model C; maximum profit $6,487; 0 hr left over in the fabrication department, 3.5 hr left over in the assembly department, 0 hr left over in the finishing department
• C) 76 units of model A, 60 units of model B, 60 units of model C; maximum profit $8,932; 1 hr left over in the fabrication department, 0 hr left over in the assembly department, 2 hr left over in the finishing department
• D) 60 units of model A, 0 units of model B, 76 units of model C; maximum profit $12,850; 0 hr left over in the fabrication department, 3 hr left over in the assembly department, 12 hr left over in the finishing department

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Definitions:

Pareto Optimal

A situation or allocation of resources from which it is impossible to reallocate to make any one individual better off without making at least one individual worse off.

Marginal Rate of Substitution

The rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility, reflected in the slope of an indifference curve.

Wheat

A cereal grain that is a staple food in many parts of the world, used to make products like bread, pasta, and flour.

Milk

A nutrient-rich liquid food produced by the mammary glands of mammals, commonly consumed by humans as a beverage or used in food production.