A furniture store has set aside 810 square feet to display its sofas and chairs. Each sofa utitizes 55 sq. fi., and each chair utilizes 35 sq. ft. At least seven sofas and at least seven chairs are to be displayed. (Let s be the number of sofas and c be the number of chalrs.) (a) Write a mathernatical model representing the store's constraints. total space used required number of sofas required number of chairs (b) Suppose the profit on sofas is $240 and on chairs is $140. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives: (i) Maxamize the total pieces of furniture displayed. Max (ii) Maximize the total expected number of daily sales. Max (iii) Maximize the total expected daily profit (in dollars)