problem 3 and problem 4 problem 3 can be solved independently and problem 4 require data from question 3.

[P3]( 2) A manufacturing plant determines how many units of standard toys and luxury toys to produce using the available machines. The first machine has the capacity to produce 300 standard toys, or 250 luxury toys per hour. The second machine can produce 400 standard toys, or 100 luxury toys. i.e. it takes 1/400 of an hour to produce a single standard toy, and 1/100 of an hour to produce a single luxury toy from machine 2). Regular toys sell for $50 and costs $20 per item, and luxury toys sell for $120 and costs $45 per item to produce. How would you determine the production schedule to maximize profit? Formulate the problem, do not solve. (for this problem only, assume you can sell all you produce) [P4] Refer to the manufacturing plant in P3. Assume that you will be operating the same plant for the next 8 hours. Your plant also has an inventory capacity of 500 toys (i.e. assume that the luxury and standard toy box dimensions are the same), and hourly unit inventory cost is $3 per hour. Demand for standard and luxury toys are given below: Hour 1 23 6 7 8 Standard Toys 600 700 400 1100 100 500 1100 100 Luxury Toys 100 250 200 400 200 150 100 500 You cannot sell more than the demand at any time period. Determine the production and inventory schedule that would maximize profit. Formulate, do not solve