Duke Earl Selling price of $2,000 per pair. Monthly demand of 35 pairs. Each pair requires 15 direct labour hours and 10 square feet of leather to produce. Selling price of $1,500 per pair Monthly demand of 50 pairs. Included in monthly demand are 30 pairs the company is required by contract to sell to a local department store with the remaining 20 pairs of demand coming from various customers. Each pair requires 10 direct labour hours and 8 square feet of leather to produce. Other Information EA does not carry inventory. "Monthly demand" represents the number of pairs customers are willing to buy per month. EA's monthly rent is $6,000 per month plus 5% of sales. EA employs 5 production staff (direct labour) who are each paid a fixed monthly salary of $5,000. Each production employee works 160 hours per month. EA's supply of leather is limited to 600 square feet per month, costing $75 per square foot. Required: Note: Each question below is independent. (a) Linear Programming: Using formulas where D = Number of Pairs of Duke Produced and E = Number of Pairs of Earl Produced: Determine the objective function, assuming EA's objective is to maximize contribution margin (1 mark) Identify all constraint functions to satisfy the above objective in a linear programming analysis (3 marks) (b) Ignoring all constraints, determine EA's monthly break-even sales in dollars, assuming that 100% of demand can be satisfied. (2 marks) (c) Determine the optimal monthly production levels of the Duke and Earl, assuming that EA is not constrained by its supply of leather (i.e. EA can purchase all the leather it requires for production at $75 per square foot). (3 marks) (d) In addition to its monthly supply of 600 square feet, EA can purchase leather from Cordo, an alternative supplier. Leather supplied by Cordo can only be used to produce the Duke but due to its lower quality, 20% of the leather purchased will be lost as waste during the production process. Determine the price EA is willing to pay Cordo per square foot of leather such that EA will earn a contribution ratio of 45% on the pairs of Duke produced from the Cordo leather. Assume that EA is not constrained by labour hours. (2 marks)