A company makes two items, I1 and I2, from three raw materials, M1, M2, and M3. Item I1 uses 3 ounces of M1, 2 ounces of M2, and 2 ounces of M3. Item I2 uses 4 ounces of M1, 1 ounce of M2, and 3 ounces of M3. The profit on item I1 is $8 and on item I2 is $6. The company has a daily supply of 40 ounces of M1, 20 ounces of M2, and 60 ounces of M3.
(a) How many of items I1 and I2 should be made each day to maximize profit?
(b) What is the maximum profit?
(c) How many ounces of each raw material are used?
(d) If the profit on item I1 increases to $13, how many of items I1 and I2 should be made each day to maximize profit?