### Problem B.11: Production-Mix DecisionEach coffee table produced by Kevin Watson Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Watson’s firm is small, and its resources are limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.**Task:** Formulate Watson’s production-mix decision as a linear programming problem, and solve it. Determine how many tables and bookcases should be produced each week and calculate the maximum profit. [PX]**Detailed Analysis:**- **Resource Constraints:** - Varnish: 10 gallons available - Redwood: 12 lengths available- **Product Requirements:** - Coffee Table: - 1 gallon of varnish - 1 length of redwood - Profit: $9 - Bookcase: - 1 gallon of varnish - 2 lengths of redwood - Profit: $12**Objective:** Maximize profit by determining the optimal number of coffee tables and bookcases that can be produced within the given resource constraints.

Here, I would formulate the LP, which is stated below, The number of coffee table=X1 The number of…

Answered: Formulate Watson's production-mix…

Practical Management Science

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

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Formulate Watson's production-mix decision as a linear programming problem, and solve. How many tables and bookcases should be produced each week? What will the maximum profit be? [PX]