our company makes hand sanitizer in two lines: Moisturizing+, and StandardSoap. On the market, Moisturizing+ retails for $175/L and StandardSoap retails for $95/L. You make the hand sanitizer by combining lotion, soap, and secret ingredient SpecialX. These ingredients are purchased from a mysterious supplier, and you can purchase at most 4000L of lotion, 5000L of soap, and 750L of SpecialX in a month. Lotion costs $25/L, soap costs $10/L, and SpecialX costs $35/L. To make 1L of Moisturizing+, you need to combine 0.5L of lotion, 0.3L of soap, and 0.2L of SpecialX. To make 1L of StandardSoap, you need to combine 0.4L of lotion, 0.55L of soap, and 0.05L of SpecialX. Your company has committed to donating 500L of StandardSoap to a local charity. Since this is a donation, you will not receive any revenue. However, the costs and purchasing limits apply to both the hand sanitizer that is sold on the market and donated to charity. You want to maximize your monthly profit. Assume that demand is high and you can sell all your hand sanitizer at the current level of resources. Write down the linear program to determine the optimal production mix, then set up the Excel spreadsheet and use Solver to compute the optimal production mix.
Your company makes hand sanitizer in two lines: Moisturizing+, and StandardSoap. On the market, Moisturizing+ retails for $175/L and StandardSoap retails for $95/L.
You make the hand sanitizer by combining lotion, soap, and secret ingredient SpecialX. These ingredients are purchased from a mysterious supplier, and you can purchase at most 4000L of lotion, 5000L of soap, and 750L of SpecialX in a month. Lotion costs $25/L, soap costs $10/L, and SpecialX costs $35/L.
To make 1L of Moisturizing+, you need to combine 0.5L of lotion, 0.3L of soap, and 0.2L of SpecialX. To make 1L of StandardSoap, you need to combine 0.4L of lotion, 0.55L of soap, and 0.05L of SpecialX.
Your company has committed to donating 500L of StandardSoap to a local charity. Since this is a donation, you will not receive any revenue. However, the costs and purchasing limits apply to both the hand sanitizer that is sold on the market and donated to charity.
You want to maximize your monthly profit.
Assume that demand is high and you can sell all your hand sanitizer at the current level of resources. Write down the linear program to determine the optimal production mix, then set up the Excel spreadsheet and use Solver to compute the optimal production mix.
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