gible, or untidy. Problem 1. A furniture store sells 4 types of furnitures: dining tables, small tables, blue sofas, and green sofas. The store owner wants to maximize the total profit of selling them. The profit of these furnitures is $450 for each dining table, $125 for each small desk, $600 for each blue sofa, and $260 for each green sofa. There are two types of cost for making furnitures: the cost of the material and labour cost (i.e. salaries of workers). The cost of making each furniture is listed in the following table. Type of furnitures Cost Material Labour Cost Dining Table $850 $150 Small Desk $560 $90 Blue Sofa $3500 $200 Green Softa $3200 $300 For example, to make a dining table, the cost is $850 for the material, and $150 for the labour cost. The store owner wants to maximize the total profit, with the following two budget constraints. Cost of material of all furnitures should be no more than $140,000. Total labour cost should be no more than $52,000. Formulate this as a Linear Programming problem. Let x,y,z, w be the number of dining tables, small desks, blue sofas, and green sofas. Your objective function will look like Maximize: 913 + 2y + 32 + cow, for appro- priate values of constants C1,C2,C3, C. The inequality constraints should express the conditions for the budget constraints. 1